Equality of immanantal decomposable tensors
type: Item
instance of: scholarly article
title: Equality of immanantal decomposable tensors
zbMATH Open document ID: 1073.15025
author: Henrique F.da Cruz
author: J. A. Dias Da Silva
published in: Linear Algebra and its Applications
publication date: 2005-06-01T00:00:00Z
review text: The concept of tensor product has been extended to the notion of symmetry class of tensors to deal with the symmetry in multilinear mappings. The authors present a necessary and sufficient condition for the equality of immanantal decomposable tensors with symmetry associated with irreducible characters of the form \((p,\dots,p)\). The exterior powers and the symmetric powers of V are immanantal symmetry classes associated with irreducible characters of this form. The conditions they present ``mix'' the avove conditions for the exterior powers and the symmetric powers. Section 3 is devoted to the study of decomposable tensors. This paper addresses conditions for equality of immanantal decomposable tensors. A theorem of the main result is given in Section 4.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 2173140
zbMATH Keywords: decomposable symmetrized tensors
zbMATH Keywords: matroid colorings
zbMATH Keywords: tensor product
zbMATH Keywords: symmetric powers
zbMATH Keywords: immanantal symmetry classes
zbMATH Keywords: irreducible characters
zbMATH Keywords: exterior powers
MaRDI profile type: Publication
full work available at URL: j.laa.2003.08.001
OpenAlex ID: W2086870146
cites work: Orthogonal decomposable symmetrized tensors
cites work: Conditions for a symmetrized decomposable tensor to be zero
cites work: On the μ-colorings of a matroid
cites work: Flags and equality of tensors
cites work: Colorings and equality of tensors
cites work: Q3676243
cites work: The Characters and Representations of Imprimitive Groups
cites work: Q4771383
cites work: Q4106341
cites work: Q4348659
cites work: Q4302493
DOI: 10.1016/J.LAA.2003.08.001
description: scientific article; zbMATH DE number 2173140