On rational algorithms for recognizing whether a matrix belongs to a congruence class

Recieved: 01/10/2023

Accepted: 03/20/2023

Published: 09/20/2023

Keywords: unitoid, cosquare, canonical form with respect to congruences, involution, Toeplitz decomposition

To cite this article

Ikramov Kh.D. On rational algorithms for recognizing whether a matrix belongs to a congruence class. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2023. N 3, p.23-26 https://doi.org/10.55959/MSU/0137–0782–15–2023–47–3–23–26.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Ikramov Kh.D. (Lomonosov Moscow State University (MSU))

Abstract

Similarity transformations are the main part of matrix theory, which studies numerous classes of special matrices. Accordingly, there are many ways of describing such classes. In most cases, one can verify whether a matrix belongs to the required class by a rational calculation, that is, by a finite algorithm using only arithmetical operations.