chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2020-21-3-84-88cheb-853Research ArticleСтатьиArticleПредставление матриц над полями в виде матриц с нулевым квадратом и диагональных матрицRepresenting Matrices over Fields as Square-Zero Matrices and Diagonal MatricesДанчевПётрDanchevPeter

доктор математики

Doctor of Mathematicks

danchev@math.bas.bgИнститут математики и информатики Болгарской ака- демии наукБолгарияInstitute of Mathematics and Informatics, Bulgarian Academy of SciencesBulgaria2020251220202138488Copyright © Данчев П., 20202020Данчев П.Danchev P.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/853

Мы доказываем, что любая квадратная матрица над произвольным бесконечным по-лем является суммой матрицы с нулевым квадратом и диагонализуемой матрицы. Этотрезультат несколько контрастирует с недавней теоремой Бреза, опубликованной в LinearAlgebra & Appl. (2018).

We prove that any square matrix over an arbitrary infinite field is a sum of a square-zeromatrix and a diagonalizable matrix. This result somewhat contrasts recent theorem due toBreaz, published in Linear Algebra & Appl. (2018).

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The authors declare that there are no conflicts of interest present.