Showing papers in "Linear Algebra and its Applications in 2004"

TL;DR: In this article, it was shown that for any positive integer n⩾3, there exist two equienergetic graphs of order 4n that are not cospectral.

TL;DR: A numerical measure of how well a frame reconstructs vectors when some of the frame coefficients of a vector are lost is introduced and the attempt to find and classify the frames that are optimal in this setting is attempted.

TL;DR: A simple algorithm is devised to speed up the computation of PageRank, in which the PageRank of pages that have converged are not recomputed at each iteration after convergence.

TL;DR: In this article, a nonlinear projection on subsemimodules is introduced, where the projection of a point is the maximal approximation from below of the point in the sub-semimmodule.

TL;DR: In this paper, the authors extend these notions to a linear transformation defined on a Euclidean Jordan algebra and study some interconnections between these extended concepts and specialize them to the space S n of all n × n real symmetric matrices with the semidefinite cone S n and the space R n with the Lorentz cone.

TL;DR: A multilinear generalization of the singular value decomposition and the best rank-R 1, R 2,…, R N approximation of higher-order tensors are reviewed.

TL;DR: A new non-linear registration model based on a curvature type smoother is introduced, within the variational framework, and it is shown that affine linear transformations belong to the kernel of this regularizer.

TL;DR: In this paper, the spectral radius of the adjacency matrix and the Laplacian matrix of a simple undirected graph is analyzed in terms of the degrees and the 2-degrees of vertices.

TL;DR: A.S. Markov as discussed by the authors extended the weak law of large numbers and the central limit theorem to certain sequences of dependent random variables forming special classes of what are now known as Markov chains.

TL;DR: This paper presents an O(nk) procedure, Algorithm MR3, for computing k eigenvectors of an n×n symmetric tridiagonal matrix T, and shows that if each representation satisfies three prescribed conditions then the computed eigenvesctors are orthogonal to working accuracy and have small residual norms with respect to the original matrix T.

TL;DR: In this paper, it was shown that the 3-term recurrence, difference equation, Askey-Wilson duality, and orthogonality can be obtained in a uniform manner from the corresponding Leonard pair.

TL;DR: In this article, the classical system of matrix equations A 1 XB 1 =C 1, A 2 XB 2 =C 2 over R, an arbitrary regular ring with identity, is considered.

TL;DR: In this paper, the authors considered the problem of finding the monic Jacobi matrix associated with the three canonical perturbations in terms of the so-called Jacobi matrices associated with a quasi-definite linear functional.

TL;DR: In this paper, the blind identification of linear mixtures of independent random processes is related to the diagonalization of some tensors, and the problem is posed in terms of a non-conventional joint approximate diagonalization.

TL;DR: For trees, the relationship between minimum rank and path cover number is completely understood as mentioned in this paper, however, for non-trees only sporadic results are known, and for graphs obtained from edge-sums, and formulae for minimum rank of vertex sums of graphs.

TL;DR: In this article, the authors give explicit representations of commuting families of unitary matrices whose eigenvectors solve the MUB problem and give formulas from which the orthogonal bases can be readily computed.

TL;DR: In this article, a sufficient condition for convexity of the joint numerical range for arbitrary m and n was formulated in terms of the largest eigenvalue of an associated family of hermitian matrices parameterized by the (m − 1)-dimensional unit sphere.

TL;DR: The nonnegative inverse eigenvalue problem (NIEP) as discussed by the authors is the problem of determining necessary and sufficient conditions in order that σ be the spectrum of an entrywise nonnegative n × n matrix.

TL;DR: For n-tuples over the algebraic system, concepts such as linear dependence, space and basis may be defined by analogy with classical linear algebra by constructing spaces with bases of arbitrary cardinality.

TL;DR: In this paper, the weighted logarithmic matrix norm is defined and the bounds of the matrix exponential are obtained using the weighted lognormal norm, which are sharper than those based on the 2-logarithm matrix norm.

TL;DR: This paper is a continuation of the 2004 paper “Max-algebra and pairwise comparison matrices”, in which the max-eigenvector of a symmetrically reciprocal matrix was used to approximate such a matrix by a transitive matrix.

TL;DR: In this article, it was shown that A∈Cn×n is R-symmetric (R-skew symmetric) if RAR=A (RAR=−A).

TL;DR: In this article, a nonnegative matrix C with spectrum ( λ 1, λ 2, λ m, μ 2,…, μ n ) was constructed, where μ 1 is the Perron eigenvalue of B.

TL;DR: A simple and self-contained proof of Burnside's theorem that every proper algebra of matrices over an algebraically closed field has a non-trivial invariant subspace is given in this paper.

TL;DR: It is shown that the class of positive semidefinite symmetric nonnegative matrices V generated via a Soules basis admit for every 1⩽ r ⩽rank( V), a nonnegative factorization WH which coincides with the best approximation in the Frobenius norm to V in R n,n of rank not exceeding r.

TL;DR: In this article, the authors studied the spectral radius of graphs with n vertices and k cut edges and showed that the maximal spectral radius is obtained uniquely at K k, where K k n is a graph obtained by joining k independent vertices to one vertex of Kn−k.

TL;DR: In this article, it was shown that A and AT are ∗ congruent over any field F of characteristic not two with involution a↦ a (the involution can be the identity).

TL;DR: In this paper, the minimum degree, maximum degree and clique number of a non-commutative commutative ring was obtained for any finite field F, where the commuting graph of R is a graph with vertex set R ⧹ Z (R), and two distinct vertices a and b are adjacent if ab ǫ=ǫ.

TL;DR: In this paper, the authors present new results on the invertibility of the sum of projectors, and new relations between the nonsingularity of the difference and the sum-of-projectors.

TL;DR: The existence theorems for matrix approximations of low Kronecker rank for some classes of function-related matrices including important specimens from potential theory are given in this paper.