Power normal matrices. Issue 20 (19th December 2022)

• Record Type: Journal Article
• Authors: Furtado, Susana; Johnson, Charles R.
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 20(2022)
• Page Start: 5423
• Page End: 5432
• Publication Date: 2022-12-19
• Subjects: Eventually normal -- k-diagonal -- k-Hermitian -- k-normal -- matrix powers; 15A23 -- 15B57; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1917499
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : Over a general field and for an arbitrary positive integer k, those triangular matrices whose k th power is diagonal are explicitly characterized. This is then used to characterize those complex matrices whose k th power is normal. This gives corresponding results for matrices whose k th power is Hermitian or real symmetric. Our results generalize and imply a recent result about eventually normal and eventually Hermitian matrices.