Geodesic
On some decompositions of matrices over algebraically closed and finite fields
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 547-553

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Decomposition of every square matrix over an algebraically closed field or over a finite field into a sum of a potent matrix and a nilpotent matrix of order 2 is considered. This can be related to our recent paper, published in Linear Multilinear Algebra (2022). The question of when each square matrix over an infinite field can be decomposed into a periodic matrix and a nilpotent matrix of order 2 is also completely considered.
Keywords: field.
Mots-clés : nilpotent matrix, potent matrix, Jordan normal form, rational form 
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Peter Danchev. On some decompositions of matrices over algebraically closed and finite fields. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 547-553. http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a0/