Generalized symmetric tensors and related topics
type: Item
instance of: scholarly article
title: Generalized symmetric tensors and related topics
zbMATH Open document ID: 0846.15012
DOI: 10.1016/0024-3795(94)00136-7
author: Ming-Peng Gong
published in: Linear Algebra and its Applications
publication date: 1996-04-28T00:00:00Z
review text: For \(T= \sum_{\sigma\in G} M(\sigma) \otimes {\mathcal P} (\sigma)\), where \(M\) is a unitary matrix representation of the group \(G\) as unitary linear operators on a space \(U\), and \({\mathcal P} (\sigma)\) the permutation operator on \(W= \otimes^n V\), a generalized symmetric tensor is defined as a tensor of the form \(T(u \otimes w)\), where \(u\in U\) and \(w\) is a decomposable tensor of \(W\). The author discusses the properties of generalized symmetric tensors. The conditions for two generalized symmetric tensors to be equal are obtained. Finally, a new characterization of the set \(A\) satisfying \({\mathcal M} (AX)= {\mathcal M} (X)\) for arbitrary \(X\) with \({\mathcal M} (A)= \sum_{\sigma\in G} M(\sigma) \prod^n_{i=1} a_{i\sigma (i)}\) is presented.
reviewed by: Yang Yingchen
Mathematics Subject Classification ID: 15A72
zbMATH DE Number: 871261
zbMATH Keywords: unitary linear operator
zbMATH Keywords: permutation operator
zbMATH Keywords: endomorphism
zbMATH Keywords: generalized symmetric tensor
zbMATH Keywords: decomposable tensor
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00136-7
OpenAlex ID: W2000256924
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description: scientific article; zbMATH DE number 871261