On Some Decompositions of Matrices over Algebraically Closed and Finite Fields

DOI10.17516/1997-1397-2021-14-5-547-553zbMath1495.15020OpenAlexW4205519439MaRDI QIDQ5071383

Peter V. Danchev

Publication date: 21 April 2022

Published in: Journal of Siberian Federal University. Mathematics & Physics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/jsfu939

zbMATH Keywords

nilpotent matrixJordan normal formfieldpotent matrixrational form

Mathematics Subject Classification ID

Factorization of matrices (15A23) Matrices over special rings (quaternions, finite fields, etc.) (15B33) 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

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• 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
• Matrices over a commutative ring as sums of three idempotents or three involutions
• Certain Properties of Square Matrices over Fields with Applications to Rings
• Decompositions of matrices into potent and square-zero matrices

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