Zhang, Wen Hou, Jinchuan
Published in
Linear Algebra and Its Applications

Let A1 and A2 be standard operator algebras on complex Banach spaces X1 and X2, respectively. For k⩾2, let (i1,…,im) be a sequence with terms chosen from {1,…,k}, and assume that at least one of the terms in (i1,…,im) appears exactly once. Define the generalized product T1⁎T2⁎⋯⁎Tk=Ti1Ti2⋯Tim on elements in Ai. Let Φ:A1→A2 be a map with the range co...

Rukhin, Andrew L.
Published in
Linear Algebra and Its Applications

In the random effects model of meta-analysis for heterogeneous multidimensional data a canonical representation of the restricted likelihood function is obtained. This representation is related to a linear data transform which is based on the algebraic characteristics of error covariance matrices which are supposed to commute. The relationship betw...

Matejaš, Josip Hari, Vjeran
Published in
Linear Algebra and Its Applications

The relative accuracy of the Kogbetliantz method for computing the singular value decomposition of real triangular matrices is considered. Sharp relative error bounds for the computed singular values are derived. The results are obtained by estimating the norms of scaled perturbation matrices arising from errors generated in one step and one batch ...

Duggal, B.P. Djordjević, S.V. Kubrusly, C.S.
Published in
Linear Algebra and Its Applications

Given Banach space operators Ai,Bi∈B(X), 1⩽i⩽2, let ΦAB∈B(B(X)) denote the elementary operator ΦAB(X)=A1XB1−A2XB2. Then ΦAB has finite ascent ⩽1 for a number of fairly general choices of the operators Ai and Bi. This information is applied to prove some necessary and sufficient conditions for the range of ΦAB to be closed and in deciding conditions...

Camacho, L.M. Cañete, E.M. Gómez, J.R. Omirov, B.A.
Published in
Linear Algebra and Its Applications

The descriptions (up to isomorphism) of naturally graded p-filiform Leibniz algebras and p-filiform (p⩽3) Leibniz algebras of maximum length are known. In this paper we study the gradation of maximum length for p-filiform Leibniz algebras. The present work aims at the classification of complex p-filiform (p⩾4) Leibniz algebras of maximum length.

Moon, J.W. Shuai, Zhisheng van den Driessche, P.
Published in
Linear Algebra and Its Applications

Several relations involving closed walks and closed cycles in a weighted digraph are established. These relations are used to derive new expressions for target reproduction numbers for controlling the spectral radius of nonnegative matrices. The results are illustrated by an application to infectious disease control.

Cirici, Joana
Published in
Linear Algebra and Its Applications

We study the varieties of invariant totally geodesic submanifolds of isometries of the spherical, Euclidean and hyperbolic spaces in each finite dimension. We show that the dimensions of the connected components of these varieties determine the orbit type (or the z-class) of the isometry. For this purpose, we introduce the Segre symbol of an isomet...

Baksalary, Oskar Maria Trenkler, Götz
Published in
Linear Algebra and Its Applications

Two measures of separation between two subspaces of a finite dimensional complex vector space are introduced and investigated. The measures were inspired by known expressions for the cosines of the angle and minimal angle between subspaces and are based on the Frobenius norm. By using partitioned representations of a pair of orthogonal projectors, ...

Qi, Xiaofei Hou, Jinchuan
Published in
Linear Algebra and Its Applications

Let k be a positive integer and R a ring having unit 1. Denote by Z(R) the center of R. Assume that the characteristic of R is not 2 and there is an idempotent element e∈R such that R satisfies aRe={0}⇒a=0, aR(1−e)={0}⇒a=0, Z(eRe)k=Z(eRe) and Z((1−e)R(1−e))k=Z((1−e)R(1−e)). Then every additive map f:R→R is k-commuting if and only if f(x)=αx+h(x) fo...

Papež, J. Liesen, J. Strakoš, Z.
Published in
Linear Algebra and Its Applications

In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain. Since the discretized algebraic problems are not solved exactly, a natural question is whether the spatial distribution of the al...