Showing papers in "Linear Algebra and its Applications in 2002"

TL;DR: In this article, the authors give a characterization of the set of all completely positive, trace-preserving maps Φ: M 2 → M 2 from which one can easily check any tracepreserving map for complete positivity.

TL;DR: In this article, a continuous-time, linear descriptor system with state-delay is considered and sufficient conditions for delay-dependent/delay-independent stability and L 2 -gain analysis are obtained in terms of linear matrix inequalities (LMIs).

TL;DR: The resulting approach is completely automatic once an error tolerance is specified and also yields an error bound and thus directly provides a reduced order model and a reduced basis for the original system.

TL;DR: In this article, the generalized spectral radius is shown to be locally Lipschitz continuous on the space of compact irreducible sets of matrices, and sufficient conditions for the existence of extremal norms are obtained.

TL;DR: In this article, the authors survey recent and also older results on nonsymmetric matrix Riccati differential equations and their corresponding algebraic variants, and cite various applications connected with matrix RICCati equations.

TL;DR: In this paper, the authors generalize the previously known necessity conditions from the more restrictive case of folding paper flat (into R 2 ), and show that if the crease pattern is foldable, then the product (in a non-intuitive order) of the associated rotational matrices is the identity matrix.

TL;DR: In this article, the authors give a new approach to the problem of finding the smallest integer t for which the secant variety of projective t -spaces fills the ambient projective space.

TL;DR: In this paper, the maximal and minimal ranks of the matrix expression A 1 − B 1 X 1 C 1 − C 2 X 2 C 2 with respect to X 1 and X 2 are presented.

TL;DR: In this paper, the authors studied the matrices Q k of in-forests of a weighted digraph and their connections with the Laplacian matrix L of the digraph.

TL;DR: In this paper, a random gradient bundle method for approximating local minimizers is introduced, motivated by recent work on nonsmooth analysis of the spectral abscissa of a matrix.

TL;DR: In this paper, the existence of constant solutions with bi-skew (symmetric) constrains for generalized Sylvester equations over a finite dimensional central algebra is studied.

TL;DR: In this article, G-graded polynomial identities of the p×p matrix algebra Mp(K) over a field K of characteristic 0 graded by an arbitrary group G were studied.

TL;DR: Improvements are offered for the efficiency and applicability of preconditioners on linear algebra problems over finite fields, but most results are valid for entries from arbitrary fields.

TL;DR: In this article, the largest eigenvalue of a tree in terms of the number of vertices and the size of matchings has been shown to be upper bounded in a tree with a given size of matching.

TL;DR: In this article, a class of block structured matrices R ={ R ij } i, j = 1 N with a property that the solution of the corresponding system Rx = y of linear algebraic equations may be performed for O( N ) arithmetic operations.

TL;DR: In this article, sufficient conditions for the existence and uniqueness of a positive semidefinite solution are derived for the nonlinear matrix equation X+A ∗ F (X)A=Q.

TL;DR: In this paper, it was shown that the main eigenvalues and corresponding eigenvectors of a graph determine those of its complement, and generalize to any eigenvalue.

TL;DR: In this paper, it was shown that the problem of determining if a given integer linear recurrent sequence has a zero-a problem that is known as "Pisot's problem" is NP-hard.

TL;DR: In this article, conditions regarding some matrices involved in the solution of positive difference-algebraic systems are described, and Geometrical conditions are used to characterize positive structural properties.

TL;DR: Two matrix versions of Graeffe's iteration for matrix polynomials and cyclic reduction for block Toeplitz matrices are introduced and their convergence properties are analyzed.

TL;DR: In this article, the authors define pseudospectra for rectangular matrix poly-nomials expressed in homogeneous form and give lower bounds for the distance to the nearest nonregular polynomial and the nearest uncontrollable dth order system with equality for standard state-space systems.

TL;DR: The distance to the nearest non-hyperbolic or non-elliptic n x n QEP is shown to be the solution of a global minimization problem with n - 1 dearees of freedom.

TL;DR: In this paper, it was shown that the equality 1/Z(L#)=a(G) does not necessarily imply that 1/z(L #) satisfies the vertex connectivity constraint.

TL;DR: In this paper, the dynamic observer-based output feedback control for uncertain time-delay systems with time-varying delays is investigated, and a delay-independent dynamic observer based feedback control is proposed such that the feedback-controlled system is globally stable if some mild conditions are met.

TL;DR: In this paper, generalized Lyapunov equations with special right-hand sides have been applied in stability theory and control problems for descriptor systems, including matrix pencils, and generalized stability theorems.

TL;DR: In this paper, a representation for nonnegative definite matrix polynomials is obtained, which is used to characterize moment points by properties of generalized Hankel matrices, and an explicit representation of the orthogonal polynomial with respect to a given matrix measure is derived.

TL;DR: In this article, it was shown that a bijective map φ form A, a standard operator algebra on a Banach space of dimension > 1, onto a ring that satisfies φ(AB+BA)=φ(A)φ (B)+ φ (A,B∈ A) is additive.

TL;DR: In this article, it was proved that a graph whose (0, 1) -adjacency matrix has the spectrum of P n, the complement of the path on n vertices, must be P n.

TL;DR: In this article, the maximal energy of a bipartite n-vertex graph is determined for various classes of unicyclic bipartitite graphs, and the graphs with maximal energy are determined.

TL;DR: In this article, the controllability properties and the Lie algebra structure of networks of particles with spin immersed in an electro-magnetic field are studied and compared. And the controLLability notions, including the possibility of driving the evolution operator and/or the state, are equivalent.