Permutation equivalence and the Hermite invariant
type: Item
instance of: scholarly article
title: Permutation equivalence and the Hermite invariant
zbMATH Open document ID: 0872.15007
DOI: 10.1016/S0024-3795(97)81114-7
author: Cynthia J. Wyels
published in: Linear Algebra and its Applications
publication date: 1997-05-19T00:00:00Z
review text: This paper introduces a new invariant -- the Hermite invariant -- for testing permutation equivalence, along with a method for computing it and an assessment of its complexity. Under a restricted definition, the complexity of the invariant becomes polynomial in the dimensions of the input matrices. The sufficiency of the invariant is discussed, and experimental results are given. These results suggest that the Hermite invariant is particularly good at distinguishing nonpermutation equivalent matrices with constant row and column sums. Permutation equivalence and permutation congruence are special cases of matrix equivalence and similarity. Many normal or canonical forms have been developed to identify matrices belonging to the same equivalence or similarity classes. The situation is quite different when attempting to determine the permutation equivalence or permutation congruence of given matrices. The paper contains 6 sections: 1. Introduction, 2. The Hermite invariant, 3. Complexity and computation of the Hermite invariant, 4. The Hermite invariants of the direct sum, 5. Sufficiency of the Hermite invariant, 6. Results determined through use of the Hermite invariant. Experimental results demonstrate the value of the Hermite invariant. Section 6 discusses the determination of non-permutation-equivalence of seven sets of matrices whose status could not be determined using conventional techniques.
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 1011340
zbMATH Keywords: determinantal divisors
zbMATH Keywords: experimental results
zbMATH Keywords: normal form
zbMATH Keywords: Hermite invariant
zbMATH Keywords: permutation equivalence
zbMATH Keywords: complexity
zbMATH Keywords: permutation congruence
zbMATH Keywords: matrix equivalence
zbMATH Keywords: similarity
zbMATH Keywords: canonical forms
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
cites work: Q4777304
cites work: Matrix Analysis
cites work: Q5668937
description: scientific article; zbMATH DE number 1011340