On normal and binormal matrices

Recieved: 06/29/2022

Accepted: 11/04/2022

Published: 02/13/2023

Keywords: normal matrix, binormal matrix, unitary matrix, condition number

To cite this article

Ikramov Kh.D. On normal and binormal matrices. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2023. N 1, p.28-31 https://doi.org/10.55959/MSU/0137–0782–15–2023–1–28–31.

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

We discuss how to get a normal matrix from a binormal one and, conversely, how to get a binormal matrix from a normal one via the right multiplication on a suitable unitary matrix. Let N be a normal matrix badly conditioned with respect to inversion, that is, having a large condition number cond2N. We show that, among the binormal matrices B that can be obtained from N, there is a matrix whose eigenvalues have individual condition numbers of order (cond2N)1/2.