Power normal matrices

Over a general field and for an arbitrary positive integer k, those triangular matrices whose kth power is diagonal are explicitly characterized. This is then used to characterize those complex matrices whose kth power is normal. This gives corresponding results for matrices whose kth power is Hermi...

Full description

Saved in:
Bibliographic Details
Published inLinear & multilinear algebra Vol. 70; no. 20; pp. 5423 - 5432
Main Authors Furtado, Susana, Johnson, Charles R.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 19.12.2022
Taylor & Francis Ltd
Subjects
Eventually normal
k-diagonal
k-Hermitian
k-normal
Mathematical analysis
matrix powers
Online AccessGet full text

Cover

More Information
Summary:Over a general field and for an arbitrary positive integer k, those triangular matrices whose kth power is diagonal are explicitly characterized. This is then used to characterize those complex matrices whose kth power is normal. This gives corresponding results for matrices whose kth power is Hermitian or real symmetric. Our results generalize and imply a recent result about eventually normal and eventually Hermitian matrices.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2021.1917499