Showing papers in "Linear Algebra and its Applications in 1992"

TL;DR: In this article, a characterization of the subdifferential of matrix norms from two classes, orthogonally invariant norms and operator (or subordinate) norms, is given for some special cases.

TL;DR: In this paper, it was proved that if Z is a bounded set of matrices such that all left infinite products converge, then 8 generates a bounded semigroup, and the equality of two differently defined joint spectral radii for a set of matrix matrices.

TL;DR: In this paper, necessary and sufficient conditions are given for a finite set Z to be an RCP set having a limit function M,(d) = rIT= lAd, where d = (d,,., d,,. ), which is a continuous function on the space of all sequences d with the sequence topology.

TL;DR: Linear preserver problems as discussed by the authors concern the characterization of linear operators on matrix spaces that leave certain functions, subsets, relations, etc., invariant, and a great deal of effort has been devoted to the study of this type of question since then.

TL;DR: In this article, Neville elimination is described in terms of Schur complements of matrices and used to improve some well-known characterizations of totally positive and strictly totally positive matrices.

TL;DR: Galerkin and minimal residual algorithms for the solution of Sylvester's equation AX – XB = C using Krylov subspaces for which orthogonal bases are generated by the Arnoldi process are suitable for implementation on parallel computers.

TL;DR: This paper analyzes the pseudospectra of Toeplitz matrices, and in particular relates them to the symbols of the matrices and thereby to the spectra of the associated ToePlitz and Laurent operators.

TL;DR: In this article, the authors review the recent progress in matrix stability, focusing on the great progress that has been achieved in the last decade or two, and then study recently proven sufficient conditions for stability, with particular emphasis on P -matrices.

TL;DR: The most irregular graphs according to these measures are determined for certain classes of graphs, and the two measures are shown to be incompatible for some pairs of graphs in this paper, and the most irregular graph according to the measures of the largest eigenvalue of a real (0, 1)-adjacency matrix of a graph G and the mean degree of G are determined.

TL;DR: In this article, the Hadamard and Cauchy-Schwarz inequalities were generalized to the volume of a matrix A ∈ R m×n defined by vol A ≔√∑det 2 A IJ, summing over all r × r submatrices A of A.

TL;DR: In this paper, the moduli of the eigenvalues of a complex Gaussian matrix in terms of x 2 distributions were characterized and shown to be stochastically smaller than the norm of a k × (k + 1) real Gaussian matrices.

TL;DR: In this paper, a class of positive linear maps in the three-dimensional matrix algebra, which are generalizations of the positive linear map constructed by Choi in the relation with positive semidefinite biquadratic forms, are considered.

TL;DR: In this paper, it has been shown that the inverses of these matrices are the operators which perform the Gaussian elimination steps for calculating Cholesky's factorization.

TL;DR: In this article, the authors discuss several open problems in matrix theory that arise from theoretical and practical issues in feedback control theory and the associated area of linear systems theory, including robust stability, matrix exponent and induced norms, stabilizability and pole assignability, and nonstandard matrix equations.

TL;DR: Surprisingly, this enables us to decrease the bilinear complexity of n X n matrix multiplication below the current record upper bound for the same computation over the infinite fields of complex, real, or rational numbers.

TL;DR: In this paper, the Moore-Penrose inverse of A is a convex combination of (ordinary) inverses of its maximal nonsingular submatrices, and the weights of these convex combinations are the above weights (in transposed position).

TL;DR: In this paper, the authors provide necessary and sufficient conditions for verifying generalized diagonally dominant matrices by applying the inverse of a partitioned matrix and obtain some criteria for identifying (nonsingular) M -matrices.

TL;DR: In this paper, the determinant of the GCD and LCM matrices on S was shown to be an integral matrix, and the inverses of the two matrices were calculated.

TL;DR: In this paper, a necessary and sufficient condition is given for the existence of the stabilizing solution of the discrete-time Riccati equation without any invertibility or positivity assumptions.

TL;DR: For a Hermitian matrix H with nonsingular principal submatrix A, it was shown in this article that the eigenvalues of the Moore-Penrose inverse of the Schur complement (H/A) of A in H interlace the eigens of H.

TL;DR: In this article, the Marshall and Olkin's inequality for singular values was shown to hold for positive semidefinite Hermitian matrices, where the eigenvalues of a Hermitians n by n matrix A are represented by n positive semidefinite matrices.

TL;DR: In this article, a lower bound for the smallest singular value of A ϵ n x n is given in terms of the determinant and the 2-norm of the columns and the rows of A.

TL;DR: The generalized QR factorization with or without pivoting of two matrices A and B having the same number of rows is reintroduced, and the applications are demonstrated in solving the linear equality-constrained least-squares problem and the generalized linear regression problem.

TL;DR: In this article, the generalized Moore-Penrose inverse was defined and sufficient conditions for its existence over an integral domain were given, and a generalized Cramer's rule was proposed.

TL;DR: In this article, the spectral norm bounds for the case that R and P are accretive, i.e. have positive definite Hermitian parts, with special attention to the case of a large condition of A. The results are based on the solution of the matrix Sylvester equation and for the separation of two matrices.

TL;DR: The aim of the present paper is to characterize the eigenvectors by means of the associated graph of the matrix and to give bounds for the set of all eigenavectors.

TL;DR: In this article, the problem of finding the set of Re-positive definite matrices A such that AX = B was studied. But the complexity of the matrix inverse problem was not considered.

TL;DR: In this article, the Schatten p -norm is shown to be unitarily invariant if and only if AA ∗ X = XBB ∗, where X is a matrices.

TL;DR: The purpose of this paper is to investigate a new iterative method to solve a nonsymmetric system and to compare it with GMRES, and to see problems for which this method is more efficient than GMRES.