Nonderogatory matrices as sums of idempotent and nilpotent matrices
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Publication:2197280
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
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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