Decomposable critical tensors
type: Item
instance of: scholarly article
title: Decomposable critical tensors
zbMATH Open document ID: 1090.15023
author: J. A. Dias Da Silva
author: Fátima Rodrigues
published in: Linear Algebra and its Applications
publication date: 2006-03-29T00:00:00Z
review text: It is observed that, in \(\wedge^m V\), the notions of critical element and decomposable element coincide. Known results for decomposable elements of \(\wedge^m V\) are extended to critical elements. The authors prove that a Grassmann tensor is critical if and only if it is Grassmann decomposable. This observation allow them to conclude that the first of the main theorems of this paper generalizes the well known result. They conduct a family of generalized Plücker polynomials for characterizing the set of critical decomposable tensors. Section 2 is a combinatorial tour. In Section 3, the relation between the principal result of this article and the classical results on Grassmann spaces is established. Section 4 is on pre-image families and the reach of a tensor. Section 5 is on decomposable tensors. The main purpose of Section 6 is to construct a family of polynomials characterizing the criticality of a decomposable tensor.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 5016226
zbMATH Keywords: decomposable tensors
zbMATH Keywords: Plücker polynomials
zbMATH Keywords: Grassmann tensor
zbMATH Keywords: Grassmann spaces
MaRDI profile type: Publication
full work available at URL: j.laa.2005.09.013
OpenAlex ID: W2054978754
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DOI: 10.1016/J.LAA.2005.09.013
description: scientific article; zbMATH DE number 5016226