On the mth roots of a complex matrix

Psarrakos, PJ

dc.contributor.author	Psarrakos, PJ	en
dc.date.accessioned	2014-03-01T01:18:09Z
dc.date.available	2014-03-01T01:18:09Z
dc.date.issued	2002	en
dc.identifier.issn	10813810	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14829
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dc.subject	Ascent sequence	en
dc.subject	Eigenvalue	en
dc.subject	Eigenvector	en
dc.subject	Jordan matrix	en
dc.subject	Matrix root	en
dc.title	On the mth roots of a complex matrix	en
heal.type	journalArticle	en
heal.publicationDate	2002	en
heal.abstract	If an n x n complex matrix A is nonsingular, then for every integer m > 1, A has an mth root B, i.e., Bm = A. In this paper, we present a new simple proof for the Jordan canonical form of the root B. Moreover, a necessary and sufficient condition for the existence of mth roots of a singular complex matrix A is obtained. This condition is in terms of the dimensions of the null spaces of the powers Ak (k = 0, 1, 2, . . .).	en
heal.journalName	Electronic Journal of Linear Algebra	en
dc.identifier.volume	9	en
dc.identifier.spage	32	en
dc.identifier.epage	41	en