Showing papers in "Linear Algebra and its Applications in 1995"

TL;DR: In this paper, bounds are obtained for characteristic numbers of graphs, such as the size of a maximal clique, the chromatic number, the diameter, and the bandwidth, in terms of the eigenvalues of the standard adjacency matrix or the Laplacian matrix.

TL;DR: In this paper, the authors studied several notions of stability for DLI(M), including absolute asymptotic stability (AAS), which is the property that all products of a set of linear operators on R n → ∞.

TL;DR: In particular, for polytope norms and for the Euclidean norm, explicit upper bounds are given for the least k having \g9(∑) = √ g9k( ∑)1k for some finite k as discussed by the authors.

TL;DR: In this article, it was shown that every system of polynomials satisfying some (2 N + 1)-term recurrence relation can be expressed in terms of orthonormal matrix polynomorphisms for which the coefficients are N × N matrices.

TL;DR: In this paper, the generalized spectral radius theorem for complex matrices was shown to hold for any matrix norm ρ ∈ ∑m with spectral radius ρ = 1/m.

TL;DR: In this paper, the convex set L n has 2n − 1 vertices, which are its rank one matrices, corresponding to all bipartitions of the set {1, 2, …, n}.

TL;DR: In this article, an extension of the Furuta inequality for log majorization of positive semidefinite matrices has been proposed, which ensures matrixnorm inequalities for unitarily invariant norms, which are considered as complementary to the Golden-Thompson inequality.

TL;DR: In this article, the authors studied connected regular graphs with four distinct eigenvalues, and properties and feasibility conditions of the eigen values were given, as well as some uniqueness and nonexistence results.

TL;DR: In this paper, the authors investigated some canonical eigen-sequences associated with transformations of integer sequences, such as 1, 3, 11, 49, 257, 1531, etc.

TL;DR: For any unitarily invariant norm on Hilbert-space operators, it is shown in this article that for all operators A, B, X and positive real numbers r we have ||| |A∗XB| r ||| 2 ⩽ ||||AA ∗X| r||| ||| XBB∗| r|.

TL;DR: In this article, the column (row) W 0 -pair of W 0 pairs of a square matrix is introduced and the notion of column W 0 and column W W -properties for a set of k + 1 square matrices is introduced, where k ⩾ 1.

TL;DR: In this paper, the authors analyzed one classical approach and one new approach to count the dimension of the set of n by n matrices with a given Jordan canonical form defined a subset of matrices in complex n 2 dimensional space.

TL;DR: In this article, the existence of positive solutions of a class of algebraic matrix Riccati equations with two parameters, c (0, c ⩽ 1) and α (0, α ⩾ 1), was established.

TL;DR: In this paper, the sensitivity of matrix inversion and linear systems with respect to norm-wise relative condition numbers has been investigated, and upper bounds for the sensitivity have been derived for componentwise condition numbers.

TL;DR: In this article, it was shown that for a semiprime ring A and central subring C, every C -automorphism of the ring of upper triangular matrices over C is the composite of an inner automorphism and an automomorphism induced from a C-automorphisms of A.

TL;DR: In this article, the eigenvalue and singular-value distributions for matrices S −1 n A n and C − 1 n A N are examined, where A n, S n, and C n are Toeplitz matrices, simple circulants, and optimal circulant generated by the Fourier expansion of some function f.

TL;DR: In this paper, the vertex-edge incidence matrix of an arbitrary undirected, loopless graph was completely determined and the possible minors of such a matrix were given, depending on the maximum number of vertex-disjoint odd cycles (i.e., the odd tulgeity ) of the graph.

TL;DR: In this paper, the generalized ultrametic matrices (GUM) were introduced, which is a class of nonnegative matrices which, under a simple condition, are inverse M-matrices.

TL;DR: In this article, a unified framework is presented for studying the convergence of projection methods for finding a common point of finitely many closed convex sets in R n. The resulting methods are block-iterative and hence lend themselves to parallel implementation.

TL;DR: In this article, the authors prove necessary conditions for a graph to be Hamiltonian in terms of eigenvalues of certain matrices associated with the graph and give an easy algebraic proof of the nonexistence of a Hamilton cycle in two graphs, one of them being the Petersen graph.

TL;DR: In this paper, the critical points and local minimum of the distance function f A (X ) = ∥ A − X ∥ 2 on varieties of fixed rank symmetric, skew-symmetric, and rectangular matrices X are determined.

TL;DR: In this paper, a complete set of invariants and an explicit canonical form for contragredient equivalence were developed and a sufficient condition for the existence of square roots of AB and BA was presented.

TL;DR: In this article, the spectrum of a stochastic matrix of order n + 1 if and only if there exists some real matrix B with spectrum {λ 1, …, λn} and some n-simplex S ⊂ R n containing the origin such that BS ⊈ S. This result appears implicitly in Ciarlet's work, and it provides a geometrical tool to obtain sufficient conditions for the nonnegative eigenvalue problem.

TL;DR: In this article, the authors established strong partial relationships between the real symmetric positive semidefinite (PSD) matrices and the Euclidean distance matrices, which allowed the transfer of some insights from one problem to the other and allowed computational tools for the PSD problem to be used for the distance problem.

TL;DR: In this paper, the authors present criteria for verifying the copositivity of an n × n matrix, given that all its principal submatrices of order n − 1 are copositive.

TL;DR: In this paper, various notions of multivariate functions which map families of positive semidefinite matrices or of conditionally positive semi-ideal matrices into matrices of the same type are studied.

TL;DR: In this paper, it was shown that for a certain class of functions, having f evaluated at the greatest common divisor of x i and x j as its, i, j entry is a factor of the matrix ( f [ x i, x j ] in the ring of n × n matrices over the integers.

TL;DR: In this article, the p -competition graph is defined as a digraph with vertex set V and an edge between x and y if and only if there are distinct vertices a 1, a i, a p and arcs ( x, a i ) and ( y, a I ) in D for each i ≤ p.

TL;DR: In this paper, it was shown that any partition of the coordinate set of a linear code corresponds to a set of generalized MacWilliams identities, and that a well-chosen partition yields a promising method to settle existence and uniqueness problems.

TL;DR: The generalized ultrametric matrices (GUM) as discussed by the authors are a generalization of the strictly ultrameral matrices, which were introduced by Marti´nez, Michon, and San Marti n. They proved that a nonnegative matrix is a GUM if and only if the matrix is defined by a sum of at most rank-two matrices.