Geodesic
Representing matrices over fields as square-zero matrices and diagonal matrices
Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 84-88

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that any square matrix over an arbitrary infinite field is a sum of a square-zero matrix and a diagonalizable matrix. This result somewhat contrasts recent theorem due to Breaz, published in Linear Algebra Appl. (2018).
Keywords: matrices, rational form, diagonal form, nilpotents. 
@article{CHEB_2020_21_3_a9,
     author = {P. Danchev},
     title = {Representing matrices over fields as square-zero matrices and diagonal matrices},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {84--88},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a9/}
}
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P. Danchev. Representing matrices over fields as square-zero matrices and diagonal matrices. Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 84-88. http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a9/