on copositive matrices abstract a criterion for copositive matrices is given and for n 3 the set of all copositive matrices is determined in terms of matrix elements copositive matrices are applied to the problem of excluding periodic solutions of certain algebraic differential equations

infinitely divisible nonnegative matrices m matrices and the embedding problem for finite state stationary markov chains abstract this paper explicitly details the relation between m matrices nonnegative roots of nonnegative matrices and the embedding problem for finite state stationary markov chains the set of nonsingular nonnegative matrices with arbitrary nonnegative roots is shown to be the closure of the set of matrices with matrix roots in im the methods presented here employ nothing beyond basic matrix analysis however it answers a question regarding m matrices posed over 30 years ago and as an application a new characterization of the set of all embeddable stochastic matrices is obtained as a corollary

some properties of schur complements and diagonal schur complements of diagonally dominant matrices in this paper we prove that the diagonal schur complement of a strictly doubly diagonally dominant matrix is strictly doubly diagonally dominant matrix the same holds for the diagonal schur complement of a strictly generalized doubly diagonally dominant matrix and a nonsingular h matrix we point out that under certain assumptions the diagonal schur complement of a strictly doubly doubly product diagonally dominant matrix is also strictly doubly doubly product diagonally dominant further we provide the distribution of the real parts of eigenvalues of a diagonal schur complement of h matrix we also show that the schur complement of a diagonally dominant matrix is not always diagonally dominant by a numerical example and then obtain a sufficient condition to ensure that the schur complement of a diagonally dominant matrix is diagonally dominant

sign pattern matrices that admit p0 matrices abstract for sign patterns corresponding to directed or undirected cycles we identify conditions under which the patterns admit or require p 0 matrices

temporal autocorrelation in univariate linear modeling of fmri data in functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them shaping or coloring attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering removing the autocorrelation or prewhitening gives the best linear unbiased estimator assuming that the autocorrelation is accurately known for single event designs the efficiency of the estimator is considerably higher for prewhitening compared with coloring however it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias to overcome this we consider different ways to estimate the autocorrelation for use in prewhitening after high pass filtering is performed a tukey taper set to smooth the spectral density more than would normally be used in spectral density estimation performs best importantly estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation but only within tissue type using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10 5

brief paper unconditional stability of the foschini miljanic algorithm in this note we prove the unconditional stability of the foschini miljanic algorithm our results show that the foschini miljanic algorithm is unconditionally stable convergent even in the presence of bounded time varying communication delays and in the presence of topology changes the implication of our results may be important for the design of code division multiple access cdma based wireless networks

bd splittings of matrices abstract a new matrix decomposition of real square singular matrices called b d splitting is proposed by extending the notion of b splitting 16 for nonsingular matrices then different convergence and comparison theorems for these splittings are discussed another convergence theorem using a generalized regular splitting is also proved as a result a new characterization of monotone matrices using regular splitting is obtained as a corollary

sign patterns of inverse nonnegative matrices abstract we determine here the 0 sign patterns which occur among the inverses of nonsingular entrywise nonnegative matrices these results complete a sequence of work which began with the characterization of all possible sign patterns which occur among inverses of positive matrices and the characterization in this general case is more involved to state than the earlier ones

a new characterization of inverse positive matrices abstract the author provides a new characterization of inverse positive matrices using positive splittings it is shown that a matrix m is inverse positive iff the spectral radius of all positive splittings is less than one then a single positive splitting is found called a b splitting such that m is inverse positive iff it allows for a b splitting satisfying the spectral radius bound

stability of bounded subsets of metzler sparse matrix cones abstract we study the existence of hurwitz matrices in a class of metzler sparse matrix cones where the non zero entries are constrained to be in a bounded set in particular we provide necessary and sufficient conditions for the existence of one or more hurwitz matrices in this class of sparse matrix spaces for scenarios with uniform and non uniform bounds several examples illustrate our results

upper hessenberg and toeplitz bohemians abstract a set of matrices with entries from a fixed finite population p is called bohemian the mnemonic comes from bounded height matrix of integers bohemi and although the population p need not be solely made up of integers it frequently is in this paper we look at bohemians specifically those with population 1 0 1 and sometimes other populations for instance 0 1 i 1 i more we specialize the matrices to be upper hessenberg bohemian we then study the characteristic polynomials of these matrices and their height that is the infinity norm of the vector of monomial basis coefficients focusing on only those matrices whose characteristic polynomials have maximal height allows us to explicitly identify these polynomials and give useful bounds on their height and conjecture an accurate asymptotic formula the lower bound for the maximal characteristic height is exponential in the order of the matrix in contrast the height of the matrices remains constant we give theorems about the number of normal matrices and the number of stable matrices in these families

disappearance of cusp forms in special families in his 1954 g6ttingen lectures atle selberg sb posed the question of the asymptotic density of the poles of the eisenstein series for r a cofinite non cocompact subgroup of psl 2 r the question is known to be equivalent to the asymptotic count of the number of eigenvalues for the laplacebeltrami operator d acting in l2 h r where h is the upper halfplane with hyperbolic metric in general the spectral decomposition of d consists of the continuous band 1 4 oo with multiplicity the number of cusps of h r and a discrete component possibly in 1 4 0o spanned by eigenfunctions w1i wp2 see hj1 kb lxp for the eigenvalues aj dpj ajpj o consider the spectral counting function n r ij v n 0 see dips ps2 cor 2 3 luo lu recently established the unconditional result his argument does not involve the lindel6f hypothesis deshouillers et

generalizations of matrix monotonicity and their relationships with certain subclasses of proper splittings abstract the authors revisit the notion of a row monotone matrix and obtain new results that establish relationships with certain specific types of splittings of the matrix concerned among other results analogous results for range monotone matrices are also obtained

on classes of inverse z matrices abstract recently a classification of matrices of class z was introduced by fiedler and markham this classification contains the classes of m matrices and the classes of n 0 and f 0 matrices studied by fan g johnson and smith the problem of determining which nonsingular matrices have inverses which are z matrices is called the inverse z matrix problem for special classes of z matrices such as the m and n 0 matrices there exist at least partial results i e special classes of matrices have been introduced for which the inverse of such a matrix is an m matrix or an n 0 matrix here we define a system of classes of matrices for which the inverse of each matrix of each class belongs to one class of the classification of z matrices defined by fiedler and markham moreover certain properties of the matrices of each class are established e g inequalities for the sum of the entries of the inverse and the structure of certain schur complements we also give a necessary and sufficient condition for regularity the class of inverse n 0 matrices given here generalizes the class of inverse n 0 matrices discussed by johnson all results established here can be applied to a class of distance matrices which corresponds to a nonarchimedean metric this metric arises in p adic number theory and in taxonomy

feature extraction based on the bhattacharyya distance in this paper we present a feature extraction method by utilizing an error estimation equation based on the bhattacharyya distance we propose to use classification errors in the transformed feature space which are estimated using the error estimation equation as a criterion for feature extraction the construction of linear transformation for feature extraction is conducted using an iterative gradient descent algorithm so that the estimated classification error is minimized due to the ability to predict error it is possible to determine the minimum number of features required for classification experimental results show that the proposed feature extraction method compares favorably with conventional methods

nonnegative matrices with power invariant zero patterns abstract if a is a nonsingular m matrix the elements of the sequence a k all have the same zero pattern using the drazin inverse we show that a similar zero pattern invariance property holds for a class of matrices which is larger than the generalized m matrices

the remainder estimate in spectral accumulation for degenerating hyperbolic surfaces abstract for a degenerating family of hyperbolic surfaces sl l 0 the spectrum of sl accumulates at every point of the continuous spectrum of s0 we give optimal remainder estimates for the rate of clustering of eigenvalues

on the inverse of a special schur complement abstract the inverse of a schur complement is a very useful tool in many algorithms for the computation of the matrix inversion in this paper we study the inverse of a special schur complement cd 1 b we proved that always exist some x and y such that xdy is a inverse of cd 1 b furthermore using minimal rank properties we give some explicit expressions for x y and the inverse of cd 1 b numerical examples also given

when the sign pattern of a square matrix determines uniquely the sign pattern of its inverse abstract we give a precise characterization in terms of parity digraphs of those square matrices a such that for every matrix b with the same sign pattern as a b 1 exists and has the same sign pattern as a 1

the asymptotic behavior of green s functions for degenerating hyperbolic surfaces given a degenerating family of riemann surfaces of genus g 2 it is a natural and important question to study their spectral behaviors in particular green s functions during degeneration see 9 10 17 11 13 and 5 by the uniformization theorem any riemann surface of genus g 2 has a canonical metric of constant curvature 1 from now on we call a riemann surface with this canonical metric a hyperbolic surface and a degenerating family of hyperbolic surfaces is denoted by st l 0 the degeneration of st is caused by the pinching of several simple closed geodesics 71 l 7 1 on st that is the lengths of these geodesics go to zero as l 0 let at be the laplacian of st then the kernel of at consists of functions which are constant on each connected component of st and at is invertible on the orthogonal complement of the kernel the schwartz kernel of this inverse is called the green function of st and denoted by g z w t for z w sl we would like to study the asymptotic behavior of g z w i as l o in order to compare functions on s o and st we use the harmonic map of infinite energy so s 71 l 7 l constructed by wolf el4 intuitively speaking this map z opens up each node a pair of cusps of so into a simple closed pinching geodesic of sf at first we assume that there is only one pinching geodesic l 7 of length l on s if 7 separates st then so has two components se and so z of genus g gz respectively

generalized species sampling priors with latent beta reinforcements many popular bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences however in some applications exchangeability may not be appropriate we introduce a novel and probabilistically coherent family of non exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent beta random variables we compare their theoretical clustering properties with those of the dirichlet process and the two parameters poisson dirichlet process the proposed construction provides a complete characterization of the joint process differently from existing work we then propose the use of such process as prior distribution in a hierarchical bayes modeling framework and we describe a markov chain monte carlo sampler for posterior inference we evaluate the performance of the prior and the robustness of the resulting inference in a simulation study providing a comparison with popular dirichlet processes mixtures and hidden markov models finally we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array cgh data

characterizations of sign patterns of inverse positive matrices abstract a result of johnson leighton and robinson characterizing sign patterns of real matrices with nonzero entries whose inverses are entrywise positive is generalized the restriction to matrices with nonzero entries is removed and additional five equivalent conditions are established one of them using a graph theoretical approach expedites a simple criterion for recognition of such sign patterns

segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm the finite mixture fm model is the most commonly used model for statistical segmentation of brain magnetic resonance mr images because of its simple mathematical form and the piecewise constant nature of ideal brain mr images however being a histogram based model the fm has an intrinsic limitation no spatial information is taken into account this causes the fm model to work only on well defined images with low levels of noise unfortunately this is often not the the case due to artifacts such as partial volume effect and bias field distortion under these conditions fm model based methods produce unreliable results here the authors propose a novel hidden markov random field hmrf model which is a stochastic process generated by a mrf whose state sequence cannot be observed directly but which can be indirectly estimated through observations mathematically it can be shown that the fm model is a degenerate version of the hmrf model the advantage of the hmrf model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites although mrf modeling has been employed in mr image segmentation by other researchers most reported methods are limited to using mrf as a general prior in an fm model based approach to fit the hmrf model an em algorithm is used the authors show that by incorporating both the hmrf model and the em algorithm into a hmrf em framework an accurate and robust segmentation can be achieved more importantly the hmrf em framework can easily be combined with other techniques as an example the authors show how the bias field correction algorithm of guillemaud and brady 1997 can be incorporated into this framework to achieve a three dimensional fully automated approach for brain mr image segmentation

symmetric formulation of the s procedure kalman yakubovich popov lemma and their exact losslessness conditions in the robust stability analysis of linear time invariant systems the frequency domain and uncertainty domain of interest play algebraically symmetric roles this paper presents a new formulation of the s procedure and the kyp lemma which emphasizes this symmetry the new formulation provides a novel and unified approach for understanding when the kyp lemma provides an exact lmi test for robust stability the notions of weak and strong mutual losslessness are introduced to characterize lossless s procedure and kyp lemma the new formulation has sufficient flexibility to accommodate some recent extensions of the kyp lemma including the generalized kyp lemma the kyp lemma for nd systems and the diagonal bounded real lemma for internally positive systems using the proposed framework we also provide a lossless scaled small gain test for internally positive systems which gives an alternative proof that the structured singular value for such systems with arbitrary number of scalar uncertainties can be efficiently computed

on linear copositive lyapunov functions and the stability of switched positive linear systems we consider the problem of common linear copositive lyapunov function existence for positive switched linear systems in particular we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time invariant systems several applications of this result are also given

notes on completely positive matrices abstract let a be a n n symmetric matrix and in the closure of inverse m matrices then a can be factored as a bb t for some nonnegative lower triangular n n matrix b and cp rank a n if a is a positive semidefinite 0 1 matrix then a is completely positive and cp rank a rank a if a is a nonnegative symmetric h matrix then a is completely positive and cp rank a n n 1 2 n n where is the number of connected components of the graph g a

generalized ultrametric matrices a class of inverse m matrices abstract recently marti nez michon and san marti n introduced the new class of symmetric strictly ultrametric matrices they proved that the inverse of a strictly ultrametric matrix is a strictly row and strictly column diagonally dominant stieltjes matrix here we generalize their result by introducing a class of nonsymmetric matrices calledgeneralized ultrametric matrices we give a necessary and sufficient condition for the regularity of these matrices and prove that the inverse of a nonsingular generalized ultrametric matrix is a row and column diagonally dominant m matrix we establish that a nonnegative matrix is a generalized ultrametric matrix if and only if the matrix is a certain sum of at most rank two matrices moreover we give a characterization of generalized ultrametric matrices based on weighted trees the entries of generalized ultrametric matrices then arise as certain distances between the leaves and the root of the tree

characterizations of inverse m matrices with special zero patterns in this paper we provide some characterizations of inverse m matrices with special zero patterns in particular we give necessary and sufficient conditions for k diagonal matrices and symmetric k diagonal matrices to be inverse m matrices in addition results for triadic matrices tridiagonal matrices and symmetric 5 diagonal matrices are presented as corollaries

the linear order complementarity problem the classical complementarity problem in euclidean space can be viewed alternatively as a variational inequality or as a lattice orthogonality problem generalizations of the former have been extensively studied but infinite dimensional analogues of the latter have been largely ignored moreover as we show many well known results about the classical complementarity problem are more appropriately viewed order theoretically this is particularly true of least element solutions which are central to the present study of order complementarity in vector lattices we emphasize that the lattice theoretic descriptions we employ are very useful even in the standard finite dimensional setting

sign pattern matrices that admit m n p or inverse m matrices in this paper we identify the sign pattern matrices that occur among the n matrices the p matrices and the m matrices we also address to the class of inverse m matrices and the related admissibility of sign pattern matrices problem

tridiagonal and upper triangular inverse m matrices abstract in this paper we characterize the nonnegative nonsingular tridiagonal matrices belonging to the class of inverse m matrices we give a geometric equivalence for a nonnegative nonsingular upper triangular matrix to be in this class this equivalence is extended to include some reducible matrices

inverse h matrices abstract the notion of inverse m matrices has been quite well studied and many of their properties have been documented in the literature in this article a proposal to consider the larger class of inverse h matrices is made first certain special types of real matrices are identified as inverse h matrices while these matrices are not inverse m matrices in general their definitions are inspired by matrices that are known to be inverse m matrices in the rest of the article motivated by results that hold for inverse m matrices the endeavor will be to attempt at proving corresponding results for inverse h matrices it is shown that for the full class of inverse h matrices many of these extensions are false nevertheless two subclasses of real inverse h matrices are identified where these generalizations are shown to hold

sign properties of metzler matrices with applications abstract several results about sign properties of metzler matrices are obtained it is first established that checking the sign stability of a metzler sign matrix can be either characterized in terms of the hurwitz stability of the unit sign matrix in the corresponding qualitative class or in terms the negativity of the diagonal elements of the metzler sign matrix and the acyclicity of the associated directed graph similar results are obtained for the case of metzler block matrices and metzler mixed matrices the latter being a class of metzler matrices containing both sign and real type entries the problem of assessing the sign stability of the convex hull of a finite and summable family of metzler matrices is also solved and a necessary and sufficient condition for the existence of common lyapunov functions for all the matrices in the convex hull is obtained the concept of sign stability is then generalized to the concept of ker b sign stability a problem that arises in the analysis of certain jump markov processes a sufficient condition for the ker b sign stability of metzler sign matrices is obtained and formulated using inverses of sign matrices and the concept of l matrices several applications of the results are discussed in the last section

asymptotics of the spectrum and the selberg zeta function on the space of riemann surfaces letz s r be the selberg zeta function of a compact riemann surfacer we study the behavior ofz s r asr tends to infinity in the moduli space of stable curves the main result is an estimate forz s r valid fors in a neighborhood depending only on the genus ofs 1 our analysis gives an alternate proof of the belavin knizhnik double pole result 5

time dependence of graph theory metrics in functional connectivity analysis brain graphs provide a useful way to computationally model the network structure of the connectome and this has led to increasing interest in the use of graph theory to quantitate and investigate the topological characteristics of the healthy brain and brain disorders on the network level the majority of graph theory investigations of functional connectivity have relied on the assumption of temporal stationarity however recent evidence increasingly suggests that functional connectivity fluctuates over the length of the scan in this study we investigate the stationarity of brain network topology using a bayesian hidden markov model hmm approach that estimates the dynamic structure of graph theoretical measures of whole brain functional connectivity in addition to extracting the stationary distribution and transition probabilities of commonly employed graph theory measures we propose two estimators of temporal stationarity the s index and n index these indexes can be used to quantify different aspects of the temporal stationarity of graph theory measures we apply the method and proposed estimators to resting state functional mri data from healthy controls and patients with temporal lobe epilepsy our analysis shows that several graph theory measures including small world index global integration measures and betweenness centrality may exhibit greater stationarity over time and therefore be more robust additionally we demonstrate that accounting for subject level differences in the level of temporal stationarity of network topology may increase discriminatory power in discriminating between disease states our results confirm and extend findings from other studies regarding the dynamic nature of functional connectivity and suggest that using statistical models which explicitly account for the dynamic nature of functional connectivity in graph theory analyses may improve the sensitivity of investigations and consistency across investigations

monotonicity and positivity of coefficients of power series expansions associated with newton and halley methods for the matrix pth root abstract if a is a matrix with all eigenvalues in the disk z 1 1 the principal pth root of a can be computed by newton s method or halley s method the study of newton s method and halley s method for the matrix pth root can be done through a study of power series expansions of some sequences of scalar functions in this paper we prove monotonicity results for the coefficients in the power series expansions for both newton s method and halley s method and for all integer p 2 the sign patterns of these coefficients can be seen directly from the monotonicity results we then use these monotonicity results and their consequences to obtain some new error estimates in the matrix case to obtain a monotonic convergence result when a is a nonsingular m matrix and to obtain a structure preserving result when a is a nonsingular m matrix or a real nonsingular h matrix with positive diagonal entries

matrices and the linear complementarity problem the paper is a collection of results on the linear complementarity problem q m the results are stated in terms of the matrix m

stability of switched systems a lie algebraic condition we present a sucient condition for asymptotic stability of a switched linear system in terms of the lie algebra generated by the individual matrices namely if this lie algebra is solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of linear systems satisfying this condition possesses a quadratic common lyapunov function we also discuss the implications of this result for switched nonlinear systems c 1999 elsevier science b v all rights reserved

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

n matrix completion problem abstract an n n matrix is called an n matrix if all principal minors are negative in this paper we are interested in n matrix completion problems that is when a partial n matrix has an n matrix completion in general a combinatorially or non combinatorially symmetric partial n matrix does not have an n matrix completion here we prove that a combinatorially symmetric partial n matrix has an n matrix completion if the graph of its specified entries is a 1 chordal graph we also prove that there exists an n matrix completion for a partial n matrix whose associated graph is an undirected cycle

criteria for sign regularity of sets of matrices abstract we consider matrix intervals with respect to a certain checkerboard partial ordering we show that every real matrix contained in a matrix interval is sign regular if two special matrices taken from that matrix interval are sign regular

a note on recursive schur complements block hurwitz stability of metzler matrices and related results it is known that the stability of a metzler matrix can be characterized in a routh hurwitz like fashion based on a recursive application of scalar schur complements 1 our objective in this brief note is to show that recently obtained stability conditions are equivalent statements of this result and can be deduced directly therefrom using only elementary results from linear algebra implications of this equivalence are also discussed and several examples are given to illustrate potentially interesting system theoretic applications of this observation

the symmetric m matrix and symmetric inverse m matrix completion problems abstract the symmetric m matrix and symmetric m 0 matrix completion problems are solved and results of johnson and smith linear algebra appl 290 1999 193 are extended to solve the symmetric inverse m matrix completion problem 1 a pattern i e a list of positions in an n n matrix has symmetric m completion i e every partial symmetric m matrix specifying the pattern can be completed to a symmetric m matrix if and only if the principal subpattern r determined by its diagonal is permutation similar to a pattern that is block diagonal with each diagonal block complete or in graph theoretic terms if and only if each component of the graph of r is a clique 2 a pattern has symmetric m 0 completion if and only if the pattern is permutation similar to a pattern that is block diagonal with each diagonal block either complete or omitting all diagonal positions or in graph theoretic terms if and only if every principal subpattern corresponding to a component of the graph of the pattern either omits all diagonal positions or includes all positions 3 a pattern has symmetric inverse m completion if and only if its graph is block clique and no diagonal position is omitted that corresponds to a vertex in a graph block of order 2 the techniques used are also applied to matrix completion problems for other classes of symmetric matrices

on inverse m matrices abstract we generalize a previous result of lewin and neumann and present a characterization of inverse m matrices the approach is mainly graph theoretical

the spectrum of the hodge laplacian for a degenerating family of hyperbolic three manifolds we consider a sequence m i of compact hyperbolic manifolds converging to a complete hyperbolic manifold mq with cusps the laplace operator acting on the space of l2 differential forms on m0 has continuous spectrum filling the half line 0 oo one expects therefore that the spectra of this operator on m accumulate to produce the continuous spectrum of the limiting manifold we prove that this is the case and obtain a sharp estimate of the rate of accumulation

z matrices and inverse z matrices abstract we consider z matrices and inverse z matrices i e those nonsingular matrices whose inverses are z matrices recently fiedler and markham introduced a classification of z matrices this classification directly leads to a classification of inverse z matrices among all classes of z matrices and inverse z matrices the classes of m matrices n 0 matrices f 0 matrices and inverse m matrices inverse n 0 matrices and inverse f 0 matrices respectively have been studied in detail here we discuss each single class of z matrices and inverse z matrices as well as considering the whole classes of z matrices and inverse z matrices we establish some common properties of the classes such as eigenvalue bounds and determinant inequalities and we give a new characterization of some classes of z matrices and inverse z matrices moreover we prove that other classes besides those of m matrices n 0 matrices and f 0 matrices consist of matrices whose determinants have the same sign some of the results generalize known results for m matrices n 0 matrices and f 0 matrices and for inverse m matrices inverse n 0 matrices and inverse f 0 matrices however we also show that some properties of the specific classes mentioned above do not hold for all classes of z matrices and inverse z matrices

sign patterns of matrices and their inverses abstract we study the sign pattern relationship between a matrix and its inverse to do so we examine the graph whose vertices are the sign pattern matrices and whose edges connect those which are possible sign patterns of a matrix and its inverse we have bounds for the degree connectivity radius and diameter of this graph in addition we have the complete description for the 3 3 case

positive path product and inverse m matrices it is known that an inverse m matrix is strict path product but not necessarily vice versa for n 3 it is shown that any square positive matrix may be made strict path product by predictable additions to the diagonal and that any normalized strict path product matrix may be made inverse m by additions to the diagonal that are bounded in terms of the size of the matrix the latter has implications for pairs of inverse m matrices whose hadamard product is inverse m a determinantal inequality relating principal minors and certain associated almost principal minors is derived for normalized inverse m matrices

inverse m matrices abstract this is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of m matrices and is aimed at an audience conversant with basic ideas of matrix theory a theme is the parallels anddifferences between the class of m matrices and the class of inverse m matrices among the primary tools used are diagonal multiplications the neumann expansion and the form of the inverse of a partitioned matrix some of the results seem not to have appeared before and several unsolved problems are mentioned

a convex characterization of robust stability for positive and positively dominated linear systems we provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems in particular we show that the structured singular value is always equal to its convex upper bound for nonnegative matrices and we use this result to derive necessary and sufficient linear matrix inequality lmi conditions for robust stability that involve only the system s static gain we show how this approach can be applied to test the robust stability of the foschini miljanic algorithm for power control in wireless networks in presence of uncertain interference

improved optimization for the robust and accurate linear registration and motion correction of brain images linear registration and motion correction are important components of structural and functional brain image analysis most modern methods optimize some intensity based cost function to determine the best registration to date little attention has been focused on the optimization method itself even though the success of most registration methods hinges on the quality of this optimization this paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can and do get trapped in local minima to address this problem two approaches are taken 1 to apodize the cost function and 2 to employ a novel hybrid global local optimization method this new optimization method is specifically designed for registering whole brain images it substantially reduces the likelihood of producing misregistrations due to being trapped by local minima the increased robustness of the method compared to other commonly used methods is demonstrated by a consistency test in addition the accuracy of the registration is demonstrated by a series of experiments with motion correction these motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods

some inheritance properties for complementary basic matrices abstract we say that the product of a row vector and a column vector is intrinsic if there is at most one non zero product of corresponding coordinates analogously we speak about intrinsic product of two or more matrices as well as about intrinsic factorizations of matrices since all entries of the intrinsic product are products of entries of the multiplied matrices there is no addition the class of complementary basic matrices cb matrices was recently introduced as matrices if of order n a g i 1 g i 2 g i n 1 where i 1 i 2 i n 1 is a permutation of 1 2 n 1 and the matrices g k k 1 n 1 have the form g k i k 1 c k i n k 1 for some 2 2 matrices c k it was observed that 1 independently of the permutation all such matrices with given c i s have the same spectrum though they do not form a similarity class 2 the classical companion matrix belongs to the class of cb matrices m fiedler a note on companion matrices linear algebra appl 372 2003 325 331 9 3 the multiplication of the g i s is intrinsic we explore connections between the 2 2 matrices c k and the resulting cb matrix g k in particular which properties are inherited from the c k to the g k we consider two situations for the ordinary real cb matrices and for the corresponding sign pattern matrices

almost principal minors of inverse m matrices abstract it is well known that if an inverse m matrix has a 0 entry then it must be reducible and thus have many more 0 entries this property is actually a special case of a deeper phenomenon that might be loosely described as relations among vanishing almost principal minors in an inverse m matrix this phenomenon encompasses both minors of nested dimension a certain loose monotonicity and minors of the same size in loosely related positions this phenomenon is limited to almost principal minors and where possible converses and examples are given to show the limit of the extent of this phenomenon it is also shown that if one almost principle minor is contained in another then the magnitude of the former is larger than that of the latter

copositive matrices and definiteness of quadratic forms subject to homogeneous linear inequality constraints abstract a symmetric matrix c is called copositive if the quadratic form x cx is nonnegative for all nonnegative values of the variables x 1 x 2 x n x a known sufficient condition for a quadratic form x qx to be positive unless x 0 subject to the linear inequality constraints ax 0 is that there should exist a copositive matrix c such that q a ca is positive definite the main result of this paper establishes the necessity of this condition for x qx to be merely nonnegative subject to ax 0 the situation is less straightforward the necessity of the existence of a copositive matrix c such that q a ca is positive semidefinite is proved only under various additional hypotheses regarding the size or rank of a and counterexamples are given to show that in general no such matrix may exist even when slater s constraint qualification holds our approach to these existence questions also furnishes certain tests for positivity or mere nonnegativity of x qx subject to ax 0 in which specific symmetric matrices constructed by rational operations from a and q and depending upon a single real parameter v must be tested for positive definiteness or strict copositivity for large values of v this technique is illustrated by several examples

a characterization of weak monotone matrices abstract we provide some characterizations of weak monotone matrices by using positive splittings we prove that a matrix allowing a generalized b splitting is weak monotone iff the associated spectral radius is less than one next we prove that weak monotone matrices allow a generalized b splitting weak monotonicity is associated with strong positive solvability of a linear system ax b b 0

sign stability of positive markov jump linear systems abstract this paper investigates stability of positive markov jump linear systems pmjlss in the absence of a numerical realization it considers the situation when only signs and not magnitudes of the entries of the subsystem matrices and the markov transition matrices are known the result is an analysis of a qualitative notion of stability known as sign stability although the notions of sign stability of pmjlss are natural extensions of standard stochastic stability concepts such as exponential almost sure mean and mean square stability the sign stability notions are proven equivalent which is not the case for their corresponding standard concepts moreover for irreducible markov chains the particular structure of the markov chain is shown to have no bearing on sign stability

some results about inverse positive matrices abstract a nonsingular real matrix a is said to be inverse positive if all the elements of its inverse are nonnegative this class of matrices contains the m matrices from which inherit some of their properties and applications especially in economy and in the description of iterative methods for solving nonlinear systems in this paper we present some new characterizations for inverse positive matrices and we analyze when this concept is preserved by the sub direct sum of matrices

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

matrices with zero line sums and maximal rank abstract an n n sign pattern admits a matrix with zero line sums and rank n 1 if and only if it is fully indecomposable and every arc of an associated directed bipartite graph lies on a circuit this proves a conjecture of fiedler and grone made in the study of sign patterns of inverse positive matrices

theorems on schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems abstract we firstly consider the block dominant degree for i ii block strictly diagonally dominant matrix and their schur complements showing that the block dominant degree for the schur complement of an i ii block strictly diagonally dominant matrix is greater than that of the original grand block matrix then as application we present some disc theorems and some bounds for the eigenvalues of the schur complement by the elements of the original matrix further by means of matrix partition and the schur complement of block matrix based on the derived disc theorems we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and the numerical example illustrates that the iteration can compute out the results faster

linear copositive lyapunov functions for continuous time positive switched systems continuous time positive systems switching among p subsystems are introduced and a complete characterization for the existence of a common linear copositive lyapunov function for all the subsystems is provided when the subsystems are obtained by applying different feedback control laws to the same continuous time single input positive system the above characterization leads to a very easy checking procedure

allow problems concerning spectral properties of sign pattern matrices a survey abstract an n n sign pattern matrix has entries in 0 this paper surveys the following problems concerning spectral properties of sign pattern matrices sign patterns that allow all possible spectra spectrally arbitrary sign patterns sign patterns that allow all inertias inertially arbitrary sign patterns sign patterns that allow nilpotency potentially nilpotent sign patterns and sign patterns that allow stability potentially stable sign patterns relationships between these four classes of sign patterns are given and several open problems are identified

on the spectra of matrices having nonnegative sums of principal minors abstract the localization of the eigenvalues of matrices with nonnegative sums of principal minors is studied the discussion is carried out in particular for p matrices such matrices for which almost all the eigenvalues lie on the left half plane are constructed

on the stability of switched positive linear systems it was recently conjectured that the hurwitz stability of the convex hull of a set of metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching in this note we show that 1 this conjecture is true for systems constructed from a pair of second order metzler matrices 2 the conjecture is true for systems constructed from an arbitrary finite number of second order metzler matrices and 3 the conjecture is in general false for higher order systems the implications of our results both for the design of switched positive linear systems and for research directions that arise as a result of our work are discussed toward the end of the note