Nazari, A.M. Mahdinasab, F.
Published in
Linear Algebra and Its Applications

In this paper, for a given list σ of real numbers λ1,λ2,…,λn, with sum zero and some additional more technical conditions specified in the paper, we construct a Euclidean distance matrix (EDM) having σ as its list of eigenvalues, without using Hadamard matrices.

Dmytryshyn, Andrii Futorny, Vyacheslav Sergeichuk, Vladimir V.
Published in
Linear Algebra and Its Applications

Arnold (1971) [1] constructed a miniversal deformation of a square complex matrix under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We give miniversal deformations of matrices of sesquilinear ...

Zhang, Ruiming Chen, Li-Chen
Published in
Linear Algebra and Its Applications

In this work we present a method to find inverses of certain Hankel matrices. These Hankel matrices are the moment matrices associated with some well-known q-orthogonal polynomials.

Goldberg, Felix Berman, Abraham
Published in
Linear Algebra and Its Applications

We introduce a new variant of zero forcing—signed zero forcing. The classical zero forcing number provides an upper bound on the maximum nullity of a matrix with a given graph (i.e. zero-nonzero pattern). Our new variant provides an analogous bound for the maximum nullity of a matrix with a given sign pattern. This allows us to compute, for instanc...

Słowik, Roksana
Published in
Linear Algebra and Its Applications

We study products of matrices of fixed orders. We show that if g is an upper triangular matrix, finite or infinite, over a field of q elements, then g can be expressed as a product of at most four triangular matrices whose orders are divisors of q−1. This result can be applied to the general linear and to the Vershik–Kerov group. We also present so...

Yu, Guihai Zhang, Xiao-Dong Feng, Lihua
Published in
Linear Algebra and Its Applications

Let Gw be a weighted graph. The inertia of Gw is the triple In(Gw)=(i+(Gw),i−(Gw),i0(Gw)), where i+(Gw), i−(Gw), i0(Gw) are the numbers of the positive, negative and zero eigenvalues of the adjacency matrix A(Gw) of Gw including their multiplicities, respectively. i+(Gw), i−(Gw) are called the positive, negative indices of inertia of Gw, respective...

Hashemi, Behnam Tavakolipour, Hanieh Nasrollahi Shirazi, Mahsa
Published in
Linear Algebra and Its Applications

We compare the quasi-inverses of the Kronecker sum ⊞ and product ⊠ of two given square matrices A and B, with entries from an idempotent, complete and commutative dioid. We prove that (A⊞B)⁎ is greater than or equal to (A⊠B)⁎ in the sense of the canonical order, where ⁎ denotes the quasi-inverse. We also show how to reduce the computational complex...

Ernst, Oliver G. Guo, Chun-Hua Liesen, Jörg Rodman, Leiba
Published in
Linear Algebra and Its Applications

De Marchi, Stefano Usevich, Konstantin
Published in
Linear Algebra and Its Applications

We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [3, Lemma 1]. As a special case, we apply the result to Padua and Padua-like points.

Chang, Gerard Jennhwa Lin, Jephian Chin-Hung
Published in
Linear Algebra and Its Applications

This note gives counterexamples to an edge spread problem on the zero forcing number.