basic soules matrices and their applications abstract in this paper we study the properties of the basic soules matrices in r n n which are a special subclass of the n n soules matrices generated via the basic soules basis the basic soules basis has the sign pattern n and it corresponds to the vector e n r n of all 1 s the basic soules matrices are up to a multiple by a positive scalar symmetric and doubly stochastic we begin by investigating the permanents of basic soules matrices next for a nonsingular basic soules matrix a r n n we show that the matrix a a 1 which is known to be a nonsingular m matrix has a basic soules basis of eigenvectors furthermore we obtain explicit formulas for the eigenvalues of a a 1 in terms of the eigenvalues of a finally let a r n n be a basic soules matrix of spectral radius 1 and set q i a by investigating the sign pattern of the off diagonal entries of the group inverse q of q we determine when the perron root is a concave function in each of the off diagonal entries at a

the inverse eigenvalue problem for nonnegative matrices abstract let a be a nonnegative matrix with spectrum 1 2 m and b be a nonnegative matrix with spectrum 1 2 n where 1 is the perron eigenvalue of b furthermore let a maximal diagonal element of a be greater than or equal to 1 in the article we construct a nonnegative matrix c with spectrum 1 2 m 2 n this construction enables us to obtain several results on how to determine new realizable lists from known realizable lists

negativity compensation in the nonnegative inverse eigenvalue problem abstract if a set of complex numbers can be partitioned as 1 s in such a way that each i is realized as the spectrum of a nonnegative matrix say a i then is trivially realized as the spectrum of the nonnegative matrix a a i in linear algebra appl 369 2003 169 it was shown that in some cases a real set can be realized even if some of the i are not realizable themselves here we systematize and extend these results in particular allowing the sets to be complex the leading idea is that one can associate to any nonrealizable set a certain negativity n and to any realizable set a certain positivity m then under appropriate conditions if m n we can conclude that is the spectrum of a nonnegative matrix additionally we prove a complex generalization of suleimanova s theorem

on single and double soules matrices abstract until now the concept of a soules basis matrix of sign pattern n consisted of an orthogonal matrix r r n n generated in a certain way from a positive n vector which has the property that for any diagonal matrix diag 1 n with 1 n 0 the symmetric matrix a r r t has nonnegative entries only in the present paper we introduce the notion of a pair of double soules basis matrices of sign pattern n which is a pair of matrices p q each in r n n which are not necessarily orthogonal and which are generated in a certain way from two positive vectors but such that pq t i and such that for any of the aforementioned diagonal matrices the matrix a p q t also has nonnegative entries only we investigate the interesting properties which such matrices a have as a preamble to the above investigation we show that the iterates a k r k r k t generated in the course of the qr algorithm when it is applied to a r r t where r is a soules basis matrix of sign pattern n are again symmetric matrices generated by the soules basis matrices r k of sign pattern n which are themselves modified as the algorithm progresses our work here extends earlier works by soules and elsner et al

a necessary condition for the spectrum of nonnegative symmetric 5 5 matrices abstract let a be a nonnegative symmetric 5 5 matrix with eigenvalues 1 2 3 4 5 we show that if i 1 5 i 1 2 1 then 3 i 1 5 i mcdonald and neumann showed that 1 3 4 0 let 1 2 3 4 5 be a list of decreasing real numbers satisfying 1 i 1 5 i 1 2 1 2 3 i 1 5 i 3 1 3 4 0 4 the perron property that is 1 max we show that is the spectrum of a nonnegative symmetric 5 5 matrix thus we solve the symmetric nonnegative inverse eigenvalue problem for n 5 in a region for which a solution has not been known before

nonnegative matrices with prescribed spectrum and elementary divisors abstract in this paper we give new sufficient conditions for the existence and construction of nonnegative matrices with prescribed elementary divisors which drastically improve and contain some of the previous known conditions we also show how to perturb complex eigenvalues of a nonnegative matrix while keeping its nonnegativity these results allow us under certain conditions to easily decide if a given list is realizable with prescribed elementary divisors

a uniform type inverse spectrum theorem for entrywise nonnegative matrices abstract influenced by earlier results of fiedler m fiedler eigenvalues of nonnegative symmetric matrices linear algebra appl 9 1974 119 142 wuven guo wuven eigenvalues of nonnegative matrices linear algebra appl 266 1997 261 270 established interesting theorems and posed several natural questions in the inverse spectrum problem for entrywise nonnegative matrices we answer some of these of a uniform character obtaining the sharpest possible results

a map of sufficient conditions for the real nonnegative inverse eigenvalue problem abstract the real nonnegative inverse eigenvalue problem rniep is the problem of determining necessary and sufficient conditions for a list of real numbers to be the spectrum of an entrywise nonnegative matrix a number of sufficient conditions for the existence of such a matrix are known in this paper in order to construct a map of sufficient conditions we compare these conditions and establish inclusion relations or independency relations between them

a unified view on compensation criteria in the real nonnegative inverse eigenvalue problem a connection is established between the problem of characterizing all possible real spectra of entrywise nonnegative matrices the so called real nonnegative inverse eigenvalue problem and a combinatorial process consisting in repeated application of three basic manipulations on sets of real numbers given realizable sets i e sets which are spectra of some nonnegative matrix each of these three elementary transformations constructs a new realizable set this defines a special kind of realizability called c realizability and this is closely related to the idea of compensation after observing that the set of all c realizable sets is a strict subset of the set of realizable ones we show that it strictly includes in particular all sets satisfying several previously known sufficient realizability conditions in the literature furthermore the proofs of these conditions become much simpler when approached from this new point of view

coadjoint orbits vortices and clebsch variables for incompressible fluids this paper is a study of incompressible fluids especially their clebsch variables and vortices using symplectic geometry and the lie poisson structure on the dual of a lie algebra following ideas of arnold and others it is shown that euler s equations are lie poisson equations associated to the group of volume preserving diffeomorphisms the dual of the lie algebra is seen to be the space of vortices and kelvin s circulation theorem is interpreted as preservation of coadjoint orbits in this context clebsch variables can be understood as momentum maps the motion of n point vortices is shown to be identifiable with the dynamics on a special coadjoint orbit and the standard canonical variables for them are a special kind of clebsch variables point vortices with cores vortex patches and vortex filaments can be understood in a similar way this leads to an explanation of the geometry behind the hald beale majda convergence theorems for vorticity algorithms symplectic structures on the coadjoint orbits of a vortex patch and filament are computed and shown to be closely related to those commonly used for the kdv and the schrodinger equations respectively

the symmetric nonnegative inverse eigenvalue problem for 5 5 matrices abstract the symmetric nonnegative inverse eigenvalue problem sniep asks when a list 1 2 n of n real numbers is the spectrum of an n n symmetric nonnegative matrix this problem is completely solved only for n 4 our main goal here is to contribute to the solution of sniep for n 5 we also give a sufficient condition for a list to be realized as the spectrum of a symmetric positive matrix

constructing new realisable lists from old in the niep abstract given a list of complex numbers 1 2 n we say that is realisable if is the spectrum of some entrywise nonnegative matrix the nonnegative inverse eigenvalue problem or niep is the problem of characterising all realisable lists given a realisable list 2 3 m where is the perron eigenvalue and 2 is real we find families of lists 1 2 n for which 1 2 n 3 4 m is realisable in addition given a realisable list i i 4 5 m where is the perron eigenvalue and and are real we find families of lists 1 2 3 4 for which 1 2 3 4 4 5 m is realisable

maximum likelihood narrow band direction finding and the em algorithm generalized em expectation maximization algorithms have been derived for the maximum likelihood estimation of the direction of arrival of multiple narrowband signals in noise both deterministic and stochastic signal models are considered the algorithm for the deterministic model yields estimates of the signal amplitudes while that for the stochastic model yields estimates of the powers of the signal both algorithms have the properties that their limit points are stable and satisfy the necessary maximizer conditions for maximum likelihood estimators it is shown via simulation that the maximum likelihood method allows for the resolution of the directions of arrival of signals at angular separation and noise levels for which other high resolution methods will not work algorithm convergence does depend on initial conditions however convergence to a global maximum has been observed in simulation when the initial estimates are within a significant fraction if one beamwidth componentwise of this maximum simulations also show that the deterministic model has a significant impact on the angle estimator performance

the nonnegative inverse eigenvalue problem from the coefficients of the characteristic polynomial ebl digraphs the nonnegative inverse eigenvalue problem niep is given a family of complex numbers 1 n find necessary and sufficient conditions for the existence of a nonnegative matrix a of order n with spectrum loewy and london r loewy d london a note on the inverse eigenvalue problems for nonnegative matrices linear and multilinear algebra 6 1978 83 90 resolved it for n 3 and for n 4 when the spectrum is real in our way of handling the niep we focus our attention on the coefficients of the characteristic polynomial of a thus the niep that we consider is given k1 k2 kn real numbers find necessary and sufficient conditions for the existence of a nonnegative matrix a of order n with characteristic polynomial xn k1xn 1 k2xn 2 kn the coefficients of the characteristic polynomial are closely related to the cyclic structure of the weighted digraph with adjacency matrix a we introduce a special type of digraph structure that we shall call ebl in which this relation is specially simple we give some results that show the interest of ebl structures we completely solve the niep from the coefficients of the characteristic polynomial for n 4 we also solve a special case of the niep for n 2p 1 with k1 kp 1 0 and p 2

ideal hydrodynamics on lie groups abstract in this paper we consider the reduction to a lie group of geodesic flows of left or right invariant metrics for a fixed value of momentum we describe the reduced vector field on the lie group as well as its right or left invariant symmetry fields the reduced vector field has an important hydrodynamic interpretation it is a stationary flow of an ideal fluid with a constant pressure we use the explicit expressions for the reduced vector field and its symmetry fields to define secondary hydrodynamics i e we study the reduction for the euler equations of an ideal fluid that describe the geodesics of a right invariant metric on a lie group s diff m of the volume preserving diffeomorphisms of a riemannian manifold m to the group s diff m for a typical coadjoint orbit we find all symmetry fields of a reduced flow and as a corollary we get a simple proof for nonexistence of new invariants of coadjoint orbits which are the integrals of local densities over the flow domain

a fast recursive algorithm for the maximum likelihood estimation of the parameters of a periodic signal describes a new recursive algorithm for the estimation of the parameters of a periodic signal in additive gaussian white noise these parameters are the period and the complex amplitudes of the harmonics present the proposed algorithm is based on recursive maximum likelihood ml algorithms for incomplete data as described by titterington 1985 and others these algorithms are of complexity o nm where n is the number of harmonics and m is the signal length the performance of the method is compared to that of the extended kalman filter with the aid of simulations

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

elgenvalues of nonnegative matrices abstract in a partial continuation of work by fiedler some spectral properties of symmetric nonnegative matrices are extended to general nonnegative matrices

orthogonal bases that lead to symmetric nonnegative matrices abstract in a paper dating back to 1983 soules constructs from a positive vector x an orthogonal matrix r which has the property that for any nonnegative diagonal matrix with nonincreasing diagonal entries the matrix r rt has all its entries nonnegative independently fiedler in 1988 showed that any symmetric irreducible nonsingular matrix whose powers are all m matrices and hence an mma matrix in the language of friedland hershkowitz and schneider must have an orthogonal matrix of eigenvectors r which has similar properties to those of r here for a given positive n vector x we investigate the structure of all orthogonal matrices r for which for any nonnegative diagonal matrix as above the matrices r rt are nonnegative up to a permutation of its columns each such r corresponds to a binary tree whose vertices are subsets of the set 1 2 n with the property that each vertex has either no successor or exactly two disjoint successors for such orthogonal matrices r and such nonsingular diagonal matrices we show that the set of matrices of the form r rt and the set of inverse mma matrices i e matrices whose inverses are mma matrices coincide using this result we establish a relation between strictly ultrametric matrices and inverse mma matrices finally we show that the qr factorization of r rt for certain such r s has a special sign pattern

on elementary divisors perturbation of nonnegative matrices abstract an outstanding result of guo w guo eigenvalues of nonnegative matrices linear algebra appl 266 1997 261 270 establishes that if the list 1 2 n is the spectrum of an n n nonnegative matrix where 1 is its perron eigenvalue and 2 r then for any t 0 the list t 1 t 2 t n is also the spectrum of a nonnegative matrix in this paper we extend the result of guo to elementary divisors in particular if a is a nonnegative matrix with spectrum then by means of two rank one perturbations we construct a modified matrix b which is also nonnegative with spectrum t and we explicitly provide the jordan canonical form of b

nonnegative realization of spectra having negative real parts abstract the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions for a list of complex numbers to be the spectrum of a nonnegative matrix in this paper the problem is completely solved in the case when all numbers in the given list except for one the perron eigenvalue have real parts smaller than or equal to zero

the spectra of nonnegative integer matrices via formal power series an old problem in matrix theory is to determine the n tuples of complex numbers which can occur as the spectrum of a matrix with nonnegative entries see bp94 chapter 4 or min88 chapter vii authors have studied the case where the ntuple is comprised of real numbers bor95 cia68 fri78 kel71 per53 sal72 sou83 sul49 the case where the matrices under consideration are symmetric fie74 jll96 and the general problem joh81 lm99 ll79 rea94 rea96 wuw97 various necessary conditions and sufficient conditions have been provided but a complete characterization is known for real n tuples only for n 4 kel71 sul49 and for complex n tuples only for n 3 ll79 motivated by symbolic dynamics boyle and handelman refocused attention on the nonzero part of the spectrum by making the following spectral conjecture bh91 bh93 see also boy93 8 and lm95 chapter 11 below a matrix a is primitive if all entries of a are nonnegative and for some n all entries of a are strictly positive also

block matrices and guo s index for block circulant matrices with circulant blocks abstract in this paper we deal with circulant and partitioned into n by n circulant blocks matrices and introduce spectral results concerning this class of matrices the problem of finding lists of complex numbers corresponding to a set of eigenvalues of a nonnegative block matrix with circulant blocks is treated along the paper we call realizable list if its elements are the eigenvalues of a nonnegative matrix the guo s index 0 of a realizable list is the minimum spectral radius such that the list up to the initial spectral radius together with 0 is realizable the guo s index of block circulant matrices with circulant blocks is obtained and in consequence necessary and sufficient conditions concerning the niep nonnegative inverse eigenvalue problem for the realizability of some spectra are given

realizability criterion for the symmetric nonnegative inverse eigenvalue problem abstract let 1 2 n a set of real numbers the real nonnegative inverse eigenvalue problem rniep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix if there exists a nonnegative matrix a with spectrum we say that is realized by a many realizability criteria for the existence of such a matrix a are known this paper shows that a realizability criterion given by the author which contains both kellogg s realizability criterion and borobia s realizability criterion is sufficient for the existence of an n n symmetric nonnegative matrix with prescribed spectrum

a characterization of trace zero nonnegative 5 5 matrices let 1 2 3 4 5 be a list of complex numbers with 1 2 3 4 5 0 necessary and sufficient conditions for the existence of an entry wise nonnegative 5 5 matrix a with spectrum are presented

existence and construction of nonnegative matrices with complex spectrum abstract the following inverse spectrum problem for nonnegative matrices is considered given a set of complex numbers 1 2 n find necessary and sufficient conditions for the existence of an n n nonnegative matrix a with spectrum our work is motivated by a relevant theoretical result of guo wuwen linear algebra appl 266 1997 261 theorem 2 1 there exists a real parameter 0 max 2 j n j such that the problem has a solution if and only if 1 0 in particular we discuss how to compute 0 and the solution matrix a for certain class of matrices a sufficient condition for the problem to have a solution is also derived

realizable lists on a class of nonnegative matrices abstract a square matrix of order n with n 2 is called permutative matrix when all its rows are permutations of the first row in this paper recalling spectral results for partitioned into 2 by 2 symmetric blocks matrices sufficient conditions on a given complex list to be the list of the eigenvalues of a nonnegative permutative matrix are given in particular we study niep and pniep when some complex elements in the lists under consideration have non zero imaginary part realizability regions for nonnegative permutative matrices are obtained a guo s realizability preserving perturbations result is obtained

constructing symmetric nonnegative matrices via the fast fourier transform abstract we derive an algorithm based on the fast fourier transform to construct a real symmetric matrix s with eigenvalues 1 2 n with eigenvector e 1 1 1 t belonging to the eigenvalue 1 we find simple conditions on the eigenvalues such that the algorithm constructs an irreducible matrix s 1 e where e is a symmetric doubly stochastic matrix

realizable lists via the spectra of block matrices abstract in this paper we present spectral results for matrices partitioned into higher order blocks where not all blocks are necessarily square using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative matrix are obtained and the corresponding matrix is constructed in particular spectral results for symmetric matrices are derived a result on guo perturbations for permutative matrices on given lists is generalized

realizable lists via the spectra of structured matrices abstract a square matrix of order n with n 2 is called a permutative matrix or permutative when all its rows up to the first one are permutations of precisely its first row in this paper the spectra of a class of permutative matrices are studied in particular spectral results for matrices partitioned into 2 by 2 symmetric blocks are presented and using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed guo perturbations on given lists are exhibited

perturbing non real eigenvalues of non negative real matrices abstract let b i c b i c 4 n be the spectrum of an entry non negative matrix and t 0 laffey t j laffey perturbing non real eigenvalues of nonnegative real matrices electron j linear algebra 12 2005 73 76 has shown that 2 t b t i c b t i c 4 n is also the spectrum of some nonnegative matrix laffey 2005 has used a rank one perturbation for small t and then used a compactness argument to extend the result to all nonnegative t in this paper a rank two perturbation is used to deduce an explicit and constructive proof for all t 0

the nonnegative inverse eigenvalue problem abstract let 1 n be a list of complex numbers the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix our purpose is to give an overview of the niep its history modern results and subproblems with particular emphasis on symmetric realizing matrices a substantial bibliography is included

isospectral flow method for nonnegative inverse eigenvalue problem with prescribed structure the nonnegative inverse eigenvalue problem is that given a family of complex numbers l l 1 l n find a nonnegative matrix of order n with spectrum l this problem is difficult and remains unsolved partially in this paper we focus on its generalization that the reconstructed nonnegative matrices should have some prescribed entries it is easy to see that this new problem will come back to the common nonnegative inverse eigenvalue problem if there is no constraint of the locations of entries a numerical isospectral flow method which is developed by hybridizing the optimization theory and steepest descent method is used to study the reconstruction moreover an error estimate of the numerical iteration for ordinary differential equations on the matrix manifold is presented after that a numerical method for the nonnegative symmetric inverse eigenvalue problem with prescribed entries and its error estimate are considered finally the approaches are verified by the numerical test results

the real nonnegative inverse eigenvalue problem is np hard abstract a list of complex numbers is realizable if it is the spectrum of a nonnegative matrix in 1949 suleimanova posed the nonnegative inverse eigenvalue problem niep the problem of determining which lists of complex numbers are realizable the version for reals of the niep rniep asks for realizable lists of real numbers in the literature there are many sufficient conditions or criteria for lists of real numbers to be realizable we will present an unified account of these criteria then we will see that the decision problem associated to the rniep is np hard and we will study the complexity for the decision problems associated to known criteria

on the comparison of some realizability criteria for the real nonnegative inverse eigenvalue problem abstract a result by brauer shows how to modify one single eigenvalue of a matrix via a rank one perturbation without changing any of the remaining eigenvalues this together with the properties of real matrices with constant row sums was exploited by the authors in a previous work in connection with the nonnegative inverse eigenvalue problem obtaining conditions which are sufficient for the existence of an entrywise nonnegative matrix with prescribed spectrum in this work we make use of brauer s theorem again to show that most of the previous results giving sufficient conditions for the real nonnegative inverse eigenvalue problem can be derived by using brauer s theorem moreover the technique is constructive and there is an algorithmic procedure to construct a matrix realizing the spectrum in particular we show that if either kellogg s realizability criterion or borobia s realizability criterion is satisfied then soto s realizability criterion is also satisfied none of the converses are true thus the condition given by soto appears to be the most general sufficient condition so far for the real nonnegative inverse eigenvalue problem

the least action principle and the related concept of generalized flows for incompressible perfect fluids the link between the euler equations of perfect incompressible flows and the least action principle has been known for a long time i solu tions can be considered as geodesic curves along the manifold of volume pre serving mappings here the shortest path problem is investigated given two different volume preserving mappings at two different times find for the inter mediate times an incompressible flow map that minimizes the kinetic energy or more generally the action in its classical formulation this problem has been solved 7 only when the two different mappings are sufficiently close in some very strong sense in this paper a new framework is introduced where gen eralized flows are defined in the spirit of l c young as probability measures on the set of all possible trajectories in the physical space then the minimiza tion problem is generalized as the continuous linear programming problem that is much easier to handle the existence problem is completely solved in this content downloaded from 157 55 39 159 on sun 18 sep 2016 05 02 20 utc all use subject to http about jstor org terms the least action principle 255 the case of the d dimensional torus it is also shown that under natural re strictions a classical solution to the euler equations is the unique optimal flow in the generalized framework finally a link is established with the concept of measure valued solutions to the euler equations 6 and an example is provided where the unique generalized solution can be explicitly computed and turns out to be genuinely probabilistic inria bp 105 78153 le chesnay cedex france this content downloaded from 157 55 39 159 on sun 18 sep 2016 05 02 20 utc all use subject to http about jstor org terms

fast construction of a symmetric nonnegative matrix with a prescribed spectrum abstract in this paper for a prescribed real spectrum using properties of the circulant matrices and of the symmetric persymmetric matrices we derive a fast and stable algorithm to construct a symmetric nonnegative matrix which realizes the spectrum the algorithm is based on the fast fourier transform

on universal realizability of spectra abstract a list 1 2 n of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix the list is said to be universally realizable ur if it is the spectrum of a nonnegative matrix for each possible jordan canonical form allowed by it is well known that an n n nonnegative matrix a is co spectral to a nonnegative matrix b with constant row sums in this paper we extend the co spectrality between a and b to a similarity between a and b when the perron eigenvalue is simple we also show that if 0 and 1 2 n is ur then 1 2 n is also ur we give counter examples for the cases 1 2 n is ur implies 1 2 3 n is ur and 1 2 are ur implies 1 2 is ur

connecting sufficient conditions for the symmetric nonnegative inverse eigenvalue problem abstract we say that a list of real numbers is symmetrically realisable if it is the spectrum of some entrywise nonnegative symmetric matrix the symmetric nonnegative inverse eigenvalue problem sniep is the problem of characterising all symmetrically realisable lists in this paper we present a recursive method for constructing symmetrically realisable lists the properties of the realisable family we obtain allow us to make several novel connections between a number of sufficient conditions developed over forty years starting with the work of fiedler in 1974 we show that essentially all previously known sufficient conditions are either contained in or equivalent to the family we are introducing

double soules pairs and matching soules bases abstract we consider two generalizations of the notion of a soules basis matrix a pair of nonsingular n n matrices p q is called a double soules pair if the first columns of p and q are positive pq t i and p q t is nonnegative for every n n nonnegative diagonal matrix with nonincreasing diagonal elements in a paper by chen han and neumann an algorithm for generating such pairs was given here we characterize all such pairs and discuss some implications of the characterization we also consider pairs of matrices u v such that u and v each consists of k orthonormal columns the first of which is positive and u v is nonnegative for every k k nonnegative diagonal matrix with nonincreasing diagonal elements we call such pairs matching soules pairs we characterize all such pairs and make some observations regarding the nonnegative matrices and generalized inverses generated by them

tannaka kreĭn duality for compact quantum homogeneous spaces ii classification of quantum homogeneous spaces for quantum su 2 we apply the tannaka kreuon duality theory for quantum homogeneous spaces developed in the first part of this series of papers to the case of the quantum sup2q groups we obtain a classification of their quantum homogeneous spaces in terms of weighted oriented graphs the equivariant maps between these quantum homogeneous spaces can be characterized by certain quadratic equations associated with the braiding on the representations of suqp2q we show that for q close to 1 all quantum homogeneous spaces are realized by coideals

guo s index for some classes of matrices abstract a permutative matrix is a square matrix such that every row is a permutation of the first row a circulant matrix is a matrix where each row is a cyclic shift of the row above to the right the guo s index 0 of a realizable list is the minimum spectral radius such that the list up to the initial spectral radius together with 0 is realizable the guo s index of some permutative matrices is obtained our results are constructive some examples designed using matlab are given at the end of the paper

spectra of principal submatrices of nonnegative matrices abstract let a be an n n nonnegative matrix with the spectrum 1 2 n and let a 1 be an m m principal submatrix of a with the spectrum 1 2 m in this paper we present some cases where the realizability of 1 2 m 1 2 s implies the realizability of 1 2 n 1 2 s and consider the question whether this holds in general in particular we show that the list 1 2 n 1 2 m is realizable

on continuity of guo wuwen function abstract we show that the functions g and g s introduced by guo wuwen in 4 are continuous and semialgebraic we use this fact to prove that the set n n of ordered n tuples of real numbers realizable by nonnegative matrices is a closed set

perturbations on constructible lists preserving realizability in the niep and questions of monov abstract in 5 the authors showed that if 1 2 2 4 n is realizable where 1 is the perron eigenvalue and 2 is non real then so too is 1 4 t 2 t 2 t 4 n they asked if 4 can be replaced by 1 or 2 or what is the least possible multiple c 1 of t in order for this perturbation to be realizable in 2 the authors showed that for n 4 one can find certain spectra for which the result holds when c 1 provided t is small in this paper we show that c 2 is best possible and we construct a realizing matrix for c 2 when t is sufficiently small we also address some questions of monov concerning the realizability of the derivative of a realizable polynomial and if such a polynomial must have positive power sums

an iterative method for exact maximum likelihood estimation of the parameters of a harmonic series a procedure is described for determining the exact maximum likelihood ml estimates of the parameters of a harmonic series i e the fundamental frequency and the amplitude and phase of each harmonic existing ml methods are only approximate in the sense that terms present due to mixing between the harmonics are ignored these terms asymptotically reduce to zero as the sample size increases to infinity it is argued that these terms can be significant for short signal lengths the application of the expectation maximization algorithm results in an iterative procedure that converges to a stationary point on the true parameter likelihood surface if global convergence results this point yields the exact ml estimates simulation studies illustrate the advantages of the method when short data lengths are used

on relationships between several classes of z matrices m matrices and nonnegative matrices abstract in this paper we establish relationships between several classes of well known matrices and some new classes of matrices we consider matrices whose powers are irreducible z matrices or m matrices these matrices are called zma matrices or mma matrices we establish a relationship between theses classe of matrices and the class of soules matrices moreover we prove that symmetric zma matrices and mma matrices are diagonally congruent to matrices that we call z sums and m sums conversely z sums and m sums are diagonally congruent to zma matrices and mma matrices this relationship exploits the structure of zma matrices and mma matrices and several well known properties of zma matrices follow immediately z sums and m sums are closely related to strictly ultrametric matrices sums we also characterize inverse zma matrices we prove that symmetric inverse zma matrices are diagonally congruent to shifted sums and that shifted sums are diagonally congruent to symmetric inverse zma matrices

invariants of the euler equations for ideal or barotropic hydrodynamics and superconductivity in d dimensions abstract the hamiltonian formalism for the euler equations of an ideal fluid superconductivity and a barotropic fluid on a d dimensional riemannian manifold is proposed we show that each of these equations has an infinite series of integrals if d is even generalized enstrophies and at least one integral if d is odd generalized helicity we prove that the magnetic hydrodynamics integral f v b is equal to the average linking number of vector fields rot v and b in terms of the ergodic theory all the invariants considered are casimir elements i e invariants of coadjoint action of the corresponding infinite dimensional lie algebras

extreme nonnegative matrices abstract an entrywise nonnegative n n matrix a is extreme if its spectrum 1 n has the property that for all 0 1 n is not the spectrum of a nonnegative matrix it is proved that if a is an extreme nonnegative matrix then there exists a nonzero nonnegative matrix y such that ay ya and at y 0 where is the hadamard or entrywise product and t denotes transpose

ruling out certain 5 spectra for the symmetric nonnegative inverse eigenvalue problem abstract a method is developed to show that certain spectra cannot be realized for the s niep it is applied in the 5 by 5 case to rule out many spectra that were previously unresolved these are all in the case of 3 positive and 2 negative eigenvalues as all other cases are now resolved for spectra of the sort we discuss a diagram is given of the spectra that are excluded here as well as those trivially realizable those realizable because of the trace 0 case and those that may also be excluded because of the j l l conditions a small region remains unresolved it is a very small fraction of the area of those spectra we consider

construction of nonnegative symmetric matrices with given spectrum abstract let 1 n be the spectrum of a nonnegative symmetric matrix a with the perron eigenvalue 1 a diagonal entry c and let 1 m be the spectrum of a nonnegative symmetric matrix b with the perron eigenvalue 1 we show how to construct a nonnegative symmetric matrix c with the spectrum 1 max 0 1 c 2 n 2 m

applications of a brauer theorem in the nonnegative inverse eigenvalue problem abstract a result by brauer which shows how to modify one single eigenvalue of a matrix without changing any of the remaining eigenvalues plays a relevant role in the study of the nonnegative inverse eigenvalue problem niep perfect in a long time ignored paper 1955 presents an extension of this result which shows how to modify r eigenvalues of a matrix of order n r n via a rank r perturbation without changing any of the n r remaining eigenvalues by using this extension perfect gives a realizability criterion for the real niep which is not contained in soto s realizability criterion in this work by extending perfect s result we give a new realizability criterion for the real niep which contains soto s criterion thus this new realizability criterion appears to be the most general sufficient condition for the real niep so far we also contribute to the solution of the symmetric niep for n 5

perturbing eigenvalues of nonnegative matrices abstract let a be an irreducible entrywise nonnegative n n matrix with eigenvalues 2 b i c 3 b i c 4 n where is the perron eigenvalue it is shown that for any t 0 there is a nonnegative matrix with eigenvalues t 2 t 3 t 4 n whenever t n t with 3 1 4 2 5 5 and n 2 25 for n 6 the result improves that of guo et al our proof depends on an auxiliary result in geometry asserting that the area of an n sided convex polygon is bounded by n times the maximum area of a triangle lying inside the polygon

an inequality for the spectra of nonnegative matrices abstract let a be a n n entrywise nonnegative matrix and let s k trace a k k 1 2 3 it is shown that if n 1 then n 2 s 3 3 ns 1 s 2 2 s 1 3 n 2 n 1 ns 2 s 1 2 3 2 is nonnegative the result is used to show that if 1 2 2 4 n is the spectrum of a nonnegative matrix where 2 is nonreal and 1 max j j 1 n then 1 t 2 t 2 t 4 n need not be realizable for all t 0 even when re 2 0

a characterization of trace zero symmetric nonnegative 5 5 matrices abstract the problem of determining necessary and sufficient conditions for a set of real numbers to be the eigenvalues of a symmetric nonnegative matrix is called the symmetric nonnegative inverse eigenvalue problem sniep in this paper we solve sniep in the case of trace zero symmetric nonnegative 5 5 matrices

adaptive comb filtering for harmonic signal enhancement a new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise the algorithm is composed of two cascaded parts the first estimates the fundamental frequency and enhances the harmonic component in the input and the second estimates the harmonic amplitudes and phases performance analysis provides new results for the asymptotic cramer rao bound crb on the parameters of harmonic signals with additive white noise results of simulations indicate that the variances of the estimates are of the same order of magnitude as the crb for sufficiently large data sets and illustrate the performance in enhancing noisy artificial periodic signals

guo perturbation for symmetric nonnegative circulant matrices abstract guo w guo eigenvalues of nonnegative matrices linear algebra appl 266 1997 261 270 sets the question if the list 1 2 n is symmetrically realizable that is is the spectrum of a symmetric nonnegative matrix and t 0 whether or not the list t 1 t 2 t 3 n is also symmetrically realizable in this paper we give an affirmative answer to this question in the case that the realizing matrix is circulant or left circulant we also give a necessary and sufficient condition for to be the spectrum of a nonnegative left circulant matrix

on the spectra of some g circulant matrices and applications to nonnegative inverse eigenvalue problem abstract a g circulant matrix a is defined as a matrix of order n where the elements of each row of a are identical to those of the previous row but are moved g positions to the right and wrapped around using number theory certain spectra of g circulant real matrices are given explicitly the obtained results are applied to nonnegative inverse eigenvalue problem to construct nonnegative g circulant matrices with given appropriated spectrum additionally some g circulant matrices are reconstructed from its main diagonal entries

a characterization of trace zero bisymmetric nonnegative 5 5 matrices abstract let 1 2 3 4 5 1 be real numbers such that i 1 5 i 0 in 16 o spector proved that a necessary and sufficient condition for 1 2 3 4 5 to be the eigenvalues of a traceless symmetric nonnegative 5 5 matrix is 2 5 0 and i 1 5 i 3 0 in this article we show that this condition is also a necessary and sufficient condition for 1 2 3 4 5 to be the spectrum of a traceless bisymmetric nonnegative 5 5 matrix