Sweeping-similarity of matrices
type: Item
instance of: scholarly article
title: Sweeping-similarity of matrices
zbMATH Open document ID: 0585.15001
DOI: 10.1016/0024-3795(86)90182-5
author: Lee Klingler
author: Lawrence S. Levy
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: This paper is partly expository. It deals with a canonical form problem for finite sets of matrices and generalizes matrix equivalence, matrix similarity, and simultaneous equivalence of pairs of matrices. A generalization of some more complicated matrix problems of the work of \textit{L. A. Nazarova} and \textit{A. V. Rojter} [Izv. Akad. Nauk SSSR, Ser. mat. 33, 65-89 (1969; Zbl 0195.043)] is also included. The paper contains sections of introductions, canonical form, applications, decomposition theorem, invariants of deleted and block cycles, and a Krull-Schmidt theorem.
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 3937340
zbMATH Keywords: block-cycle system
zbMATH Keywords: companion matrices
zbMATH Keywords: canonical form
zbMATH Keywords: matrix equivalence
zbMATH Keywords: matrix similarity
zbMATH Keywords: invariants
zbMATH Keywords: Krull-Schmidt theorem
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90182-5
OpenAlex ID: W1974978044
cites work: Matrix problems and categories of matrices
cites work: Q3261425
cites work: Modules over the integral group ring of a nonabelian group of order 𝑝𝑞
cites work: Mixed modules over ZG, G cyclic of prime order, and over related Dedekind pullbacks
cites work: Modules over Dedekind-like rings
cites work: Q5590839
cites work: Application of modules over a dyad for the classification of finite \(p\)-groups possessing an Abelian subgroup of index \(p\) and of pairs of mutually annihilating operators
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description: scientific article; zbMATH DE number 3937340