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

on the cohen macaulay property of modular invariant rings abstract if v is a faithful module for a finite group g over a field of characteristic p then the ring of invariants need not be cohen macaulay if p divides the order of g in this article the cohomology of g is used to study the question of cohen macaulayness of the invariant ring one of the results is a classification of all groups for which the invariant ring with respect to the regular representation is cohen macaulay moreover it is proved that if p divides the order of g then the ring of vector invariants of sufficiently many copies of v is not cohen macaulay a further result is that if g is a p group and the invariant ring is cohen macaulay then g is a bireflection group i e it is generated by elements which fix a subspace of v of codimension at most 2

the decomposition of lie powers let g be a group f a field of prime characteristic p and v a finite dimensional fg module let l v denote the free lie algebra on v regarded as an fg submodule of the free associative algebra or tensor algebra t v for each positive integer r let l r v and t r v be the r th homogeneous components of l v and t v respectively here l r v is called the r th lie power of v our main result is that there are submodules b 1 b 2 of l v such that for all r b r is a direct summand of t r v and whenever m geqslant 0 and k is not divisible by p the module l p mk v is the direct sum of l p m b k l p m 1 b pk l 1 b p mk thus every lie power is a direct sum of lie powers of p power degree the approach builds on an analysis of t r v as a bimodule for g and the solomon descent algebra

robust control in the gap a state space solution in the presence of a single input delay a solution is provided to the problem of sub optimal robust design in the gap for a system with a single input lag the problem is shown to reduce to two matrix algebraic riccati equations that solve an allied linear quadratic gaussian h sub 2 problem and a parameterized differential matrix riccati equation the analysis intertwines finite dimensional delay equations and distributed abstract evolution models the parameterized family of suboptimal compensators is presented in terms of a neutral equation model

on spl hscr sub spl infin control for dead time systems a mixed sensitivity spl hscr sub spl infin problem is solved for dead time systems it is shown that for a given bound on the spl hscr sub spl infin norm causal stabilizing controllers exist that achieve this bound if and only if a related finite dimensional riccati equation has a solution with a certain nonsingularity property in the case of zero time delay the riccati equation is a standard riccati equation and the nonsingularity condition is that the solution be nonnegative definite for nonzero time delay the nonsingularity condition is more involved but still allows us to obtain controllers all suboptimal controllers are parameterized and the central controller is shown to be a feedback interconnection of a finite dimensional system and a finite memory system both of which can be implemented some spl hscr sub spl infin problems are rewritten as pure rational spl hscr sub spl infin problems using a smith predictor parameterization of the controller

h infty controller design for preview and delayed systems the h infty control problem of general preview delayed systems is solved using analytic solutions of the corresponding operator riccati equations the solution to the problem can be applied to a broad range of input output delayed systems and enables the handling of preview delayed control problems the solvability condition is characterized by the roots of the transcendental equations and the control law for the general problem is given based on a predictive compensation with an integro differential observer some interpretations of typical control problems are presented based on the solvability condition and the resulting control law

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

formulas on preview and delayed h infty control a generalized hinfin control problem which covers preview and delayed control strategies is discussed based on a state space approach by introducing a hamiltonian matrix which is associated with a delay free generalized plant the analytic solution to the corresponding operator riccati equation is newly established based on the result obtained here the hinfin control problem is solved and for typical control problems e g hinfin and linear quadratic lq control for multiple input delay systems hinfin preview control some interpretations are provided on the resulting control system

free lie algebras and formal power series let g be a group and k a field if v is a graded kg module of the form v v1plus sign in circlev2plus sign in circlecdots three dots centered where each vn is finite dimensional then the free lie algebra l v acquires the structure of a graded kg module l v l1 v plus sign in circlel2 v plus sign in circlecdots three dots centered the isomorphism types of v and l v may be described by the power series ngt or equal slanted1 vn tn and ngt or equal slanted1 ln v tn with coefficients from the green ring the main object of study is the function on power series which maps vn tn to ln v tn for every graded kg module v closed formulae are given in certain cases and these are closely related to character formulae of brandt and others

on lie powers of the augmentation ideal in characteristic 2 abstract let g be a finite group k a field and v a finite dimensional kg module write l v for the free lie algebra on v the action of g on v extends naturally to l v so it becomes a kg module which is direct sum of finite dimensional submodules for a finite dimensional kg module v let i v denote the set of isomorphism classes of indecomposable direct summands of v and i l v n 1 i l n v it is natural to ask whether i l v is finite of course this is not a question unless there exist infinitely many isomorphism classes of indecomposable kg modules that is k has positive characteristic p and the sylow p subgroups of g are non cyclic and dim v 2 let k be a field of characteristic 2 and g the klein four group we write d k g for the augmentation ideal of kg for the dual of and v 1 v 2 v 3 for the three 2 dimensional induced modules from the three cyclic subgroups of g in this article we concentrate on lie powers l n of and describe the module decomposition of l 16 a module of dimension 2690010 in particular i l 16 d v 1 v 2 v 3

intervals of p matrices and related matrices we consider intervals of matrices with respect to the usual entrywise partial ordering necessary and sufficient conditions are given for an interval of matrices to contain only p matrices i e matrices having only positive principal minors or related matrices

modular lie representations of groups of prime order let k be a field of prime characteristic p and let g be a group of order p for any finite dimensional kg module v and any positive integer n let ln v denote the nth homogeneous component of the free lie k algebra generated by a basis of v then ln v can be considered as a kg module called the nth lie power of v the main result of the paper is a formula which describes the module structure of ln v up to isomorphism

lie powers of modules for groups of prime order let l v be the free lie algebra on a finite dimensional vector space v over a field k with homogeneous components l n v for n geq 1 if g is a group and v is a kg module the action of g extends naturally to l v and the l n v become finite dimensional kg modules called the lie powers of v in the decomposition problem the aim is to identify the isomorphism types of indecomposable kg modules with their multiplicities in unrefinable direct decompositions of the lie powers this paper is concerned with the case where g has prime order p and k has characteristic p as is well known there are p indecomposables denoted here by j 1 dots j p where j r has dimension r a theory is developed which provides information about the overall module structure of l v and gives a recursive method for finding the multiplicities of j 1 dots j p in the lie powers l n v for example the theory yields decompositions of l v as a direct sum of modules isomorphic either to j 1 or to an infinite sum of the form j r oplus j p 1 oplus j p 1 oplus ldots with r geq 2 closed formulae are obtained for the multiplicities of j 1 dots j p in l n j p and l n j p 1 for r p 1 the indecomposables which occur with non zero multiplicity in l n j r are identified for all sufficiently large n

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

symmetric powers of modular representations for groups with a sylow subgroup of prime order abstract let v be a representation of a finite group g over a field of characteristic p if p does not divide the group order then molien s formula gives the hilbert series of the invariant ring in this paper we find a replacement of molien s formula which works in the case that g is divisible by p but not by p 2 we also obtain formulas which give generating functions encoding the decompositions of all symmetric powers of v into indecomposables our methods can be applied to determine the depth of the invariant ring without computing any invariants this leads to a proof of a conjecture of the second author on certain invariants of gl 2 p

symmetric powers of the p 1 dimensional indecomposable module of a cyclic p group and the λ structure of its green ring let k be a field of order p and let g be a cyclic group of order pk k 2 we explicitly decompose the symmetric powers of the indecomposable kg module of dimension p 1 into indecomposable kg modules using this result for every odd prime p we give a negative answer to the conjecture posed by kouwenhoven f m kouwenhoven the structure of the green rings of cyclic p groups proc sympos pure math 47 1987 451 466

control of systems with i o delay via reduction to a one block problem in this paper the standard four block h sup spl infin control problem for systems with a single delay in the feedback loop is studied a simple procedure of the reduction of the problem to an equivalent one block problem having particularly simple structure is proposed the one block problem is then solved by the j spectral factorization approach resulting in the so called dead time compensator dtc form of the controller the advantages of the proposed procedure are its simplicity intuitively clear derivation of the dtc form of the h sup spl infin controller and extensibility to the multiple delay case

sub direct sums and positivity classes of matrices abstract it is well known that a direct sum is positive semidefinite if and only if each of the direct summands is positive semidefinite in fact it is also known that this statement remains true if positive semidefinite is replaced with doubly nonnegative completely positive totally nonnegative m matrix and p matrix etc for each of these classes we consider corresponding questions for a more general sum of two matrices of which the direct sum and ordinary sum are special cases

an innovation approach to h sub spl infin fixed lag smoothing for continuous time varying systems this note studies the finite horizon h sub spl infin fixed lag smoothing problem for linear continuous time varying systems a technique named as reorganized innovation analysis in krein space is developed to give a necessary and sufficient condition for the existence of an h sub spl infin fixed lag smoother the condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two riccati differential equations rdes one standard h sub spl infin filtering rde and one h sub 2 type of rde examples demonstrate the proposed h sub spl infin fixed lag smoother design and the fact that the existence of an h sub spl infin smoother does not depend on the solvability of h sub spl infin filtering

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

on standard h sub spl infin control of processes with a single delay this note presents a frequency domain method to solve the standard h sub spl infin control problem for processes with a single delay for a given bound on the closed loop h sub spl infin norm there exist proper stabilizing controllers that achieve this bound if and only if both the corresponding delay free h sub spl infin problem and an extended nehari problem with a delay or a one block problem are all solvable the solvability of the extended nehari problem or the one block problem is equivalent to the nonsingularity of a delay dependent matrix the solvability conditions of the standard h sub spl infin control problem with a delay are formulated in terms of the existence of solutions to two delay independent algebraic riccati equations and a delay dependent nonsingularity property all suboptimal controllers solving the three problems are respectively parameterized as a structure incorporating a modified smith predictor

the module structure of a group action on a polynomial ring a finiteness theorem consider a group acting on a polynomial ring over a finite field we study the polynomial ring as a module for the group and prove a structure theorem with several striking corollaries for example any indecomposable module that appears as a summand must also appear in low degree and so the number of isomorphism types of such summands is finite there are also applications to invariant theory giving a priori bounds on the degrees of the generators

intervals of totally nonnegative matrices totally nonnegative matrices i e matrices having all their minors nonnegative and matrix intervals with respect to the checkerboard ordering are considered it is proven that if the two bound matrices of such a matrix interval are nonsingular and totally nonnegative and in addition all their zero minors are identical then all matrices from this interval are also nonsingular and totally nonnegative with identical zero minors

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

metabelian lie powers of the natural module for a general linear group abstract consider a free metabelian lie algebra m of finite rank r over an infinite field k of prime characteristic p given a free generating set m acquires a grading its group of graded automorphisms is the general linear group g l r k so each homogeneous component m d is a finite dimensional g l r k module the homogeneous component m 1 of degree 1 is the natural module and the other m d are the metabelian lie powers of the title this paper investigates the submodule structure of the m d in the main result a composition series is constructed in each m d and the isomorphism types of the composition factors are identified both in terms of highest weights and in terms of steinberg s twisted tensor product theorem their dimensions are also given it turns out that the composition factors are pairwise non isomorphic from which it follows that the submodule lattice is finite and distributive by the birkhoff representation theorem any such lattice is explicitly recognizable from the poset of its join irreducible elements the poset relevant for m d is then determined by exploiting a 1975 paper of yu a bakhturin on identical relations in metabelian lie algebras

on the depth of the invariants of the symmetric power representations of sl2 fp abstract we study the depth of the ring of invariants of sl 2 f p acting on the n th symmetric power of the natural two dimensional representation for n p these symmetric power representations are the irreducible representations of sl 2 f p over f p we prove that when the greatest common divisor of p 1 and n is less than or equal to 2 the depth of the ring of invariants is 3 we also prove that the depth is 3 for n 3 p 7 and n 4 p 5 however for n 3 p 7 the depth is 4 and for n 4 p 5 the depth is 5 in these two exceptional cases the ring of invariants is cohen macaulay

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

frequency domain solution to delay type nehari problem this paper generalizes the frequency domain results on the delay type nehari problem in the stable case to the unstable case the solvability condition of the delay type nehari problem is formulated in terms of the nonsingularity of three matrices the optimal value c o p t is the maximal c 0 such that one of the three matrices becomes singular all sub optimal compensators are parameterized in a transparent structure incorporating a modified smith predictor

totally nonnegative cells and matrix poisson varieties we describe explicitly the admissible families of minors for the totally nonnegative cells of real matrices that is the families of minors that produce nonempty cells in the cell decompositions of spaces of totally nonnegative matrices introduced by a postnikov in order to do this we relate the totally nonnegative cells to torus orbits of symplectic leaves of the poisson varieties of complex matrices in particular we describe the minors that vanish on a torus orbit of symplectic leaves we prove that such families of minors are exactly the admissible families and we show that the nonempty totally nonnegative cells are the intersections of the torus orbits of symplectic leaves with the spaces of totally nonnegative matrices

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

cal h _ infty control and estimation problems with delayed measurements state space solutions most physical processes exhibit transport delay in the measured output and it is well known that this can have disastrous effects on system stability and performance if it is not accounted for in this paper we give necessary and sufficient conditions for existence of estimators and controllers that achieve the desired cal h infty performance criterion when such a measurement delay is present we also give the complete characterization of all controllers and estimators that achieve the desired performance criterion the necessary and sufficient conditions are easy to check and are given in terms of the familiar pair of algebraic riccati equations that appear in the nondelay versions of the corresponding cal h infty problems along with an additional riccati differential equation explicit state space formulas for the controllers and estimators are also obtained they have a linear periodic structure and are easily implementable to obtain these results we first obtain state space results for a modified nehari problem which may be of independent interest see problem 5 in section 2

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

modular lie powers and the solomon descent algebra let v be an r dimensional vector space over an infinite field f of prime characteristic p and let l n v denote the nth homogeneous component of the free lie algebra on v we study the structure of l n v as a module for the general linear group gl r f when n pk and k is not divisible by p and where r n our main result is an explicit 1 1 correspondence multiplicity preserving between the indecomposable direct summands of l k v and the indecomposable direct summands of l n v which are not isomorphic to direct summands of v n our approach uses idempotents of the solomon descent algebras and in addition a correspondence theorem for permutation modules of symmetric groups

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 test for strict sign regularity a characterization of strict sign regular matrices is obtained it is given in an algorithmic form which allows the easy construction of a test to check if a matrix is strictly sign regular the test is based on the neville elimination of several submatrices of a and requires less computational work than those which can be derived from other previously known characterizations of these matrices

some formulas in invariant theory in an earlier paper 121 the author discussed the relationship between invariants of the group g z pz in characteristic p and the classical covariants of sl 2 k in characteristic zero this is more closely studied here in the corresponding representation rings in characteristic zero the only indecomposable 1 irreducible sl 2 k modules are the r si where r is the set of homogeneous forms of degree n of the polynomial ring r k x y in characteristic p there are p indecomposable g modules i vp the corresponding representation rings are

invariance of total nonnegativity of a matrix under entry wise perturbation and subdirect sum of totally nonnegative matrices abstract a real matrix is called totally nonnegative if all of its minors are nonnegative in this paper the minors are determined from which the maximum allowable entry perturbation of a totally nonnegative matrix can be found such that the perturbed matrix remains totally nonnegative also the total nonnegativity of the first and second subdirect sum of two totally nonnegative matrices is considered

h_ infty control of discrete time systems with multiple input delays this paper is concerned with the finite horizon hinfin full information control for discrete time systems with multiple control and exogenous input delays we first establish a duality between the hinfin full information control and the h2 smoothing of a stochastic backward system in krein space like the duality between the linear quadratic regulation lqr of linear systems without delays and the kalman filtering the established duality allows us to address complicated multiple input delay problems in a simple way indeed by applying innovation analysis and standard projection in krein space in this paper we derive conditions under which the hinfin full information control is solvable an explicit controller is constructed in terms of two standard riccati difference equations of the same order as the original plant ignoring the delays as special cases solutions to the hinfin state feedback control problem for systems with delays only in control inputs and the hinfin control with preview are obtained an example is given to demonstrate the effectiveness of the proposed hinfin control design

intervals of almost totally positive matrices we consider the class of the totally nonnegative matrices i e the matrices having all their minors nonnegative and intervals of matrices with respect to the chequerboard partial ordering which results from the usual entrywise partial ordering if we reverse the inequality sign in all components having odd index sum for these intervals in 1982 we stated in this journal the following conjecture if the left and right endpoints of an interval are nonsingular and totally nonnegative then all matrices taken from the interval are nonsingular and totally nonnegative in this paper we show that this conjecture is true if we restrict ourselves to the subset of the almost totally positive 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

the invariants of the third symmetric power representation of sl2 fp abstract for a prime p 3 we compute a finite generating set for the sl 2 f p invariants of the third symmetric power representation the proof relies on the construction of an infinite sagbi basis and uses the hilbert series calculation of hughes and kemper

ia automorphisms and lie algebras related to the mccool group abstract we investigate a subgroup i n of the mccool group m n we show that i n has solvable conjugacy problem next we investigate its lie algebra gr i n and we find a presentation for it finally we show that gr i n is naturally embedded into the andreadakis johnson lie algebra of the ia automorphisms of the free group f n

another look at finite horizon h control problems for systems with input delays we discuss a finite horizon h control problem for time varying systems with input delays clarifying a relationship between two h control problems in input delay case and in measurement delay case we derive a solution in input delay case based on the known result for the h control problem in measurement delay case and show that the solution has the same predictor observer structure as the solution in measurement delay case has using this structural information on the solution we also present an elementary proof of the solution to the finite horizon h control problem for systems with input delays which is based only on completion of squares

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

an innovation approach to h prediction for continuous time systems with application to systems with delayed measurements this paper studies the problem of h prediction for linear continuous time systems by developing a new method of characterizing the innovation process and applying a novel innovation analysis approach in krein space a necessary and sufficient condition for the existence of a finite horizon h predictor is derived the solution to the h prediction is given in terms of solutions of riccati and matrix differential equations we further extend our study to give a necessary and sufficient condition for the h filtering of linear continuous time systems with both instantaneous and delayed measurements

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

the standard h sub spl infin problem in systems with a single input delay the standard h sub spl infin problem is solved for lti systems with a single pure input lag the solution is based on state space analysis mixing a finite dimensional and an abstract evolution model utilizing the relatively simple structure of these distributed systems the associated operator riccati equations are reduced to a combination of two algebraic riccati equations and one differential riccati equation over the delay interval the results easily extend to finite time and time varying problems where the algebraic riccati equations are substituted by differential riccati equations over the process time duration

h sub spl infin filtering for multiple time delay measurements the aim of this paper is to study the h sub spl infin filtering problem for linear continuous time systems with both current and multiple time delay measurements the key technique applied for deriving the filter is the reorganized innovation analysis approach in krein space a necessary and sufficient condition for the existence of an h sub spl infin filter is derived and the solution to the h sub spl infin filter is given in terms of solutions of riccati and matrix differential equations an example is finally presented to show the effectiveness of the proposed approach

subdirect sums of p p0 matrices and totally nonnegative matrices abstract in this paper the problem of when the sub direct sum of two strictly diagonally dominant p matrices is a strictly diagonally dominant p matrix is studied in particular it is shown that the subdirect sum of overlapping principal submatrices of strictly diagonally dominant p matrices is a strictly diagonally dominant p matrix it is also established that the 2 subdirect sum of two totally nonnegative matrices is a totally nonnegative matrix under some conditions it is obtained that a partial totally nonnegative matrix whose graph of the specified entries is a monotonically labeled 2 chordal graph has a totally nonnegative completion finally a positive answer to the question iv in fallat and johnson shaun m fallat c r johnson j r torregrosa a m urbano p matrix completions under weak symmetry assumptions linear algebra appl 312 2000 73 91 is given for p 0 matrices

the species and idempotents of the green algebra of a finite group with a cyclic sylow subgroup we study the green algebra a kg generated by the isomorphism classes of indecomposable kg modules where k is a field with chark p 0 and g a finite group with a cyclic sylow p subgroup more precisely we discuss the homomorphisms a kg c called species and state a formula for the idempotents of a kg

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