Structure of the \(n\)th roots of a matrix
type: Item
instance of: scholarly article
title: Structure of the \(n\)th roots of a matrix
zbMATH Open document ID: 0777.15005
DOI: 10.1016/0024-3795(93)90127-A
author: Gabriëlle ten Have
published in: Linear Algebra and its Applications
publication date: 1993-08-29T00:00:00Z
review text: The paper presents the following results: Let \(K\) be a subfield of \(C\). A criterion is given for a nonsingular matrix \(A\) in \(M_ mK\) to have an \(n\)th root in \(M_ mK\). The number of similarity classes of the \(n\)th root of \(A\) is given for \(K=R\). Further it is indicated which matrices \(A\) in \(M_ mK\) have infinitely many \(n\)th roots in \(M_ mK\).
reviewed by: Seshadri Sridhar
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 399290
zbMATH Keywords: matrix equations
zbMATH Keywords: non-singular matrix
zbMATH Keywords: \(n\)th root
zbMATH Keywords: similarity class
MaRDI profile type: Publication
cites work: On the matrix equation \(f(x)=A\)
cites work: Q3254327
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cites work: Q3243274
full work available at URL: 0024-3795(93)90127-a
OpenAlex ID: W2162306265
description: scientific article; zbMATH DE number 399290