Showing papers in "Linear Algebra and its Applications in 1994"

TL;DR: In this paper, the authors survey some of the many results known for Laplacian matrices, and present a survey of the most important results in the field of graph analysis.

TL;DR: The classical and modified Gram-Schmidt (CGS) orthogonalization is one of the fundamental procedures in linear algebra as mentioned in this paper, and it is equivalent to the factorization AQ1R, where Q1∈Rm×n with orthonormal columns and R upper triangular.

TL;DR: In this article, a log majorization result for power means of positive semidefinite matrices was obtained, which implies matrix norm inequalities for unitarily invariant norms, which are considered as complementary to the Golden-Thompson one.

TL;DR: In this paper, a formula for the inverse of a general tridiagonal matrix is given in terms of the principal minors of the matrix, where the principal minor is defined by the principal matrix.

TL;DR: It is shown that the computed approximate solution is the exact solution of a perturbed pencil, and bounds and estimates of the perturbations are given.

TL;DR: In this article, it was shown that the Laplacian spectrum of a maximal graph is the conjugate of its degree sequence, and that, apart from 0, it is the same for all maximal graphs.

TL;DR: This paper outlines some germane points in the history of the CSD, pointing out the contributions of Jordan, of Davis and Kahan, and of Stewart, and the relationship of theCSD to the “direct rotation” ofDavis and Kato.

TL;DR: In matrix theory, majorization plays a significant role as discussed by the authors, and majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities.

TL;DR: An approximation lemma is presented and it is shown that in all cases arbitrary probability vectors can be replaced by sparse ones (with only logarithmically many positive entries) without losing too much performance.

TL;DR: Fast algorithms for computing the product with a vector are presented for a number of classes of matrices whose properties relate to the properties of Toeplitz, Vandermonde, or Cauchy matrices and also for their inverses, involving factor circulants.

TL;DR: The conjecture of Fisher and Hartwig, published in 1968, describes the asymptotic expansion of Toeplitz determinants with singular generating functions as mentioned in this paper, and it has been extended several times.

TL;DR: In this article, it was shown that it is useful to regard S = sign(A) as being part of a matrix sign decomposition A = SN, where N = (A2)1/2.

TL;DR: In this paper, the Neville elimination process for nonsingular totally positive matrices has been studied in detail in the case of nonsedular matrices, and a wide class of matrices are found where Neville elimination has a lower computational cost than Gauss elimination.

TL;DR: This article presents a general description on how and when the componentwise rates differ, as well as their relationships with the global rate, and provides an example, a standard contaminated normal model, to show that such phenomena are not necessarily pathological, but can occur in useful statistical models.

TL;DR: In this paper, partial converses are obtained for Weyl's inequalities for two Hermitian matrices with property L and analogous results for the product of two positive definite Hermitians.

TL;DR: In this article, necessary and sufficient conditions for the reverse product A+n…A+2A+1 of the Moore-Penrose inverses of A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, An were given.

TL;DR: This paper proves the equivalence of these two notions of frequency response, and establishes a more direct link of the second approach to the H∞ norm, and provides the first approach with a natural interpretation of steady-state response as an infinite sum of sinusoidal signals.

TL;DR: In this paper, the basic ideas of Willems's treatment of linear systems are easily generalized to linear systems over arbitrary rings and to group systems, and the interplay between systems (behaviors) and trellises (evolution laws) is discussed with respect to completeness, minimality, controllability, and observability.

TL;DR: In this article, a perturbation analysis of the canonical correlations of matrix pairs is presented, and absolute and relative bounds for normwise and componentwise perturbations are derived.

TL;DR: The tensor product of a linear system with the quotient field of the ring of linear differential operators is a vector space where, even in the time-varying case, a (formal) Laplace transform and the transfer matrix are most naturally defined.

TL;DR: The characteristic polynomial of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the three point Chebyshev recurrence relationship.

TL;DR: In this paper, the analycity property of functions on the eigenvalues λ(z) = (λ1(z),…, λn(z)) of A(z).

TL;DR: In this article, a state-space theory for the study of linear shift-invariant finite-dimensional hybrid dynamical systems is developed, and the analysis result can be applied to any hybrid system with the proposed hybrid state space model to the optimal digital control problem for standard four-block configuration with H-norm performance measure.

TL;DR: In this article, the authors generalize an investigation of distances among random vectors begun by Olkin and Pukelsheim and continued by O'Neill and Rachev, and show that it is possible to generalize this work.

TL;DR: In this paper, it was shown that the generalized inverse of a matrix product can arise from factorizations of the matrix which is to be inverted, such as full rank factorizations, normal factorizations and singular value decompositions (SVD).

TL;DR: In this paper, the techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions and it is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadratures formula with the highest degree of precision.

TL;DR: In this paper, an algebraic derivation of the canonical form of a generic pair of projections is given, which is used to determine the spectral shift of a pair of projection and various properties of Fredholm pairs.

TL;DR: A simple method which leads to results on the Lipschitz continuity of the matrix absolute value and several new ones is discussed.

TL;DR: In this paper, the authors characterize irreducible powerful sign pattern matrices and investigate the period and base of such matrices, and give some significant classes of powerful patterns.

TL;DR: In this paper, the authors studied the asymptotic behavior of a nonhomogeneous semi-Markov system (population) in discrete time and established the conditions under which the ergodic behavior of such a chain exists and provided the limit of the basic matrix of the chain.