Representing Matrices over Fields as Square-Zero Matrices and Diagonal Matrices

Danchev, P.V.

doi:10.22405/2226-8383-2020-21-3-84-88

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2021

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Cited by 3 publications

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“…Let us consider below two situations, namely, algebraically closed fields (see Corollary 2.4) and finite fields (see Corollary 3.2). The results can be viewed and treated as the development of method and ideas presented in [8] and [6], respectively. Some closely related studies can also be found in [5].…”

Section: Introduction and Conventionsmentioning

confidence: 99%

On Some Decompositions of Matrices over Algebraically Closed and Finite Fields

Danchev¹

2021

J. Sib. Fed. Univ., Math. phys.

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We study when every square matrix over an algebraically closed field or over a finite field is decomposable into a sum of a potent matrix and a nilpotent matrix of order 2. This can be related to our recent paper, published in Linear & Multilinear Algebra (2022). We also completely address the question when each square matrix over an infinite field can be decomposed into a periodic matrix and a nilpotent matrix of order 2

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Section: Introduction and Conventionsmentioning

confidence: 99%

On Some Decompositions of Matrices over Algebraically Closed and Finite Fields

Danchev¹

2021

J. Sib. Fed. Univ., Math. phys.

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Certain Properties of Square Matrices over Fields with Applications to Rings

Danchev

2021

rev.colomb.mat

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We prove that any square nilpotent matrix over a field is a difference of two idempotent matrices as well as that any square matrix over an algebraically closed field is a sum of a nilpotent square-zero matrix and a diagonalizable matrix. We further apply these two assertions to a variation of π-regular rings. These results somewhat improve on establishments due to Breaz from Linear Algebra & amp; Appl. (2018) and Abyzov from Siberian Math. J. (2019) as well as they also refine two recent achievements due to the present author, published in Vest. St. Petersburg Univ. - Ser. Math., Mech. & amp; Astr. (2019) and Chebyshevskii Sb. (2019), respectively.

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On the idempotent and nilpotent sum numbers of matrices over certain indecomposable rings and related concepts

Danchev¹

2021

Mat. Stud.

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Representing Matrices over Fields as Square-Zero Matrices and Diagonal Matrices

Cited by 3 publications

References 1 publication

On Some Decompositions of Matrices over Algebraically Closed and Finite Fields

On Some Decompositions of Matrices over Algebraically Closed and Finite Fields

Certain Properties of Square Matrices over Fields with Applications to Rings

On the idempotent and nilpotent sum numbers of matrices over certain indecomposable rings and related concepts

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