Decompositions of matrices into diagonalizable and square-zero matrices

DOI10.1080/03081087.2020.1862742OpenAlexW3113542929MaRDI QIDQ5887664

Miguel Gómez Lozano, Esther García, Peter V. Danchev

Publication date: 13 April 2023

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2020.1862742

zbMATH Keywords

companion matrixirreducible polynomialnilpotent matrixJordan normal formdiagonalizable matrixrational form

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Canonical forms, reductions, classification (15A21) Diagonalization, Jordan forms (15A20)

Related Items (2)

Decompositions of matrices into potent and square-zero matrices ⋮ Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence

Cites Work

• Unnamed Item
• Unnamed Item
• Sums of two triangularizable quadratic matrices over an arbitrary field
• On expressing matrices over \(\mathbb{Z}_2\) as the sum of an idempotent and a nilpotent
• Matrices over finite fields as sums of periodic and nilpotent elements
• On the core-nilpotent decomposition of trees
• Nonderogatory matrices as sums of idempotent and nilpotent matrices
• A Jordan canonical form for nilpotent elements in an arbitrary ring
• The ring \(\operatorname{M}_{8 k + 4}(\mathbb{Z}_2)\) is nil-clean of index four
• On some matrix analogs of the little Fermat theorem
• Nil-clean matrix rings
• Nil clean rings.
• Primitive Polynomials Over Finite Fields
• Generators and irreducible polynomials over finite fields
• Distribution of irreducible polynomials of small degrees over finite fields
• Matrices over a commutative ring as sums of three idempotents or three involutions

This page was built for publication: Decompositions of matrices into diagonalizable and square-zero matrices