Nonderogatory matrices as sums of idempotent and nilpotent matrices

DOI10.1016/j.laa.2020.07.021zbMath1447.15029OpenAlexW3044904458MaRDI QIDQ2197280

Sergiu Megieşan, Simion Sorin Breaz

Publication date: 31 August 2020

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

Full work available at URL: https://doi.org/10.1016/j.laa.2020.07.021

zbMATH Keywords

companion matrixnilpotent matrixidempotent matrixnonderogatory matrixnil-clean decomposition

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Matrix completion problems (15A83)

Related Items (5)

Decompositions of matrices into diagonalizable and square-zero matrices ⋮ Decompositions of matrices into potent and square-zero matrices ⋮ On Some Decompositions of Matrices over Algebraically Closed and Finite Fields ⋮ Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence ⋮ Nil-clean index of \(M_n(\mathbb{F}_2)\)

Cites Work

• Sums of two square-zero matrices over an arbitrary field
• Nil-clean and strongly nil-clean rings.
• Nil-clean companion matrices
• On decomposing any matrix as a linear combination of three idempotents
• 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
• The ring \(\operatorname{M}_{8 k + 4}(\mathbb{Z}_2)\) is nil-clean of index four
• Nil-clean matrix rings
• Sums of small numbers of idempotents
• Commutators in Division Rings
• Lifting Idempotents and Exchange Rings
• On the Representation of an Idempotent as a Sum of Nilpotent Elements
• Sums of projections

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