A criterion for unitary congruence between complex matrices
type: Item
instance of: scholarly article
title: A criterion for unitary congruence between complex matrices
zbMATH Open document ID: 1260.15011
published in: Journal of Mathematical Sciences (New York)
publication date: 2012-11-28T00:00:00Z
review text: The following new theorem of unitary congruence of two matrices is proved: Let \(A,B \in {M_n}({\mathbb C})\), where \({M_n}({\mathbb C})\) is the set of complex matrices of order \(n\), and \[ \begin{aligned} &\alpha (s) = A{A^ * },\,\,\alpha (t) = {A^T}\bar A,\,\,\alpha (u) = A\bar A,\,\,\alpha (v) = {(A\bar A)^ * },\\ &\beta (s) = B{B^ * },\,\,\beta (t) = {B^T}\bar B,\,\,\beta (u) = B\bar B, \beta (v) = {(B\bar B)^ * }\end{aligned} \] be the families over the alphabet \(X = \{ s,t,u,v\}\) determined by \(A\) and \(B\). Then \(A\) and \(B\) are unitarily congruent if and only if the conditions \(tr\alpha (p) = tr\beta (p)\), which form a finite set, are fulfilled for every \(p \in {X^{2l + 1}}\) and for a certain upper bound integer \(l = l(n)\) for the length of all families in \({M_n}({\mathbb C})\).
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 6110777
zbMATH Keywords: complex matrix
zbMATH Keywords: unitary congruence
author: Yury A. Al'pin
author: Kh. D. Ikramov
MaRDI profile type: Publication
full work available at URL: s10958-012-0780-9
OpenAlex ID: W2169076260
cites work: Matrix Analysis
cites work: A complete set of unitary invariants for operators generating finite \(W^ *\)-algebras of type I
cites work: A criterion for unitary congruence between matrices
cites work: A characterization of unitary congruence
cites work: An upper bound for the length of a finite-dimensional algebra
DOI: 10.1007/S10958-012-0780-9
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description: scientific article; zbMATH DE number 6110777