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Permutation equivalence and the Hermite invariant

✍ Scribed by Cynthia J. Wyels

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
627 KB
Volume
256
Category
Article
ISSN
0024-3795

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✦ Synopsis

Permutation equivtdence and permutation congnlence are special cases of matrix equivalence and similarity. 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.

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Hermite indices and equivalence relation
Hermite indices and equivalence relations
✍ I BaragaΓ±a; V FernΓ‘ndez; I Zaballa πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 203 KB

The Hermite indices are invariant for the right equivalence of non-singular polynomial matrices and for the similarity of controllable matrix pairs. Nevertheless, they do not form a complete system of invariants. The aim of this work is to define two equivalence relations, one in the set of non-sin