De Schepper, Anneleen Van Maldeghem, Hendrik
Published in
Linear Algebra and Its Applications

We study to which extent the family of pairs of subspaces of a vector space related to each other via intersection properties determines the vector space. In another language, we study to which extent the family of vertices of the building of a projective space related to each other via several natural respective conditions involving the Weyl dista...

Shao, Meiyue
Published in
Linear Algebra and Its Applications

Computing the exponential of large-scale skew-Hermitian matrices or parts thereof is frequently required in applications. In this work, we consider the task of extracting finite diagonal blocks from a doubly-infinite skew-Hermitian matrix. These matrices usually have unbounded entries which impede the application of many classical techniques from a...

Akian, Marianne Gaubert, Stéphane Marchesini, Andrea
Published in
Linear Algebra and Its Applications

Let λ1,…,λn denote the eigenvalues of a n×n matrix, ordered by nonincreasing absolute value, and let γ1≥⋯≥γn denote the tropical eigenvalues of an associated n×n matrix, obtained by replacing every entry of the original matrix by its absolute value. We show that for all 1≤k≤n, |λ1⋯λk|≤Cn,kγ1⋯γk, where Cn,k is a combinatorial constant depending only...

Gonçalves, Vinicius Mariano Maia, Carlos Andrey Hardouin, Laurent
Published in
Linear Algebra and Its Applications

An extension to an algorithm of R.A. Cuninghame-Green and K. Zimmermann for solving equations with residuated functions is presented. This extension relies on the concept of weak residuation and in the so-called “strong property”. It is shown that a contextualization of this method to tropical linear equations, which will be denoted as Primal Metho...

Lankeit, Johannes Neff, Patrizio Nakatsukasa, Yuji
Published in
Linear Algebra and Its Applications

We show that the unitary factor Up in the polar decomposition of a nonsingular matrix Z=UpH is a minimizer for both‖Log(Q⁎Z)‖and‖sym⁎(Log(Q⁎Z))‖ over the unitary matrices Q∈U(n) for any given invertible matrix Z∈Cn×n, for any unitarily invariant norm and any n. We prove that Up is the unique matrix with this property to minimize all these norms sim...

Melman, A.
Published in
Linear Algebra and Its Applications

We generalize several Cauchy-like inclusion regions for the zeros of a polynomial expressed in a basis defined by a three-term recurrence relation. Our results are obtained by applying linear algebra techniques to the comrade matrix of a polynomial. We pay special attention to the Newton and Chebyshev bases.

Peña, J.M.
Published in
Linear Algebra and Its Applications

A matrix is almost strictly totally positive if all its minors are nonnegative and they are positive if and only if they do not contain a zero in their diagonal. An optimal test to check if a given matrix belongs to this class of matrices is presented. For this purpose, we establish a bijection between the set of nonzero entries of the matrix and a...

Aguirre Holguín, Valeria Wojciechowski, Piotr J.
Published in
Linear Algebra and Its Applications

A special class of matrix algebras, the rc-signature algebras, naturally emerged as a result of the study of a Multiplicative Decomposition Property of matrices (a multiplicative analogue of the Riesz Decomposition Property in ordered vector spaces). This note is devoted to the study of a tractable subclass of these algebras. It is proven that a ne...

Wójcik, Paweł
Published in
Linear Algebra and Its Applications

For Banach spaces we consider the bounded linear operators which are surjective and noninjective. We show some general properties of such mappings. We examine whether such operators can be restricted to an involution or a projection. Thus, we will show that there exist many invariant subspaces for those operators. In respect to this, we will unders...

Sato, Iwao
Published in
Linear Algebra and Its Applications

Recently, Bapat and Sivasubramanian [1] presented formulas for the determinant and the inverse of the product distance matrix of a tree. Furthermore, they defined a bivariant Ihara–Selberg zeta function of a graph and gave its determinant expression. We present new proofs for three results of Bapat and Sivasubramanian.