Abstract:
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:
nilpotent matrix, potent matrix, Jordan normal form, rational form, field.
The author was partially supported by the Bulgarian National Science Fund (Grant KP-06 N 32/1 of Dec. 07, 2019).
Received: 22.04.2021 Received in revised form: 29.05.2021 Accepted: 05.06.2021
Bibliographic databases:
Document Type:
Article
UDC:
512.6
Language: English
Citation:
Peter Danchev, “On some decompositions of matrices over algebraically closed and finite fields”, J. Sib. Fed. Univ. Math. Phys., 14:5 (2021), 547–553
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\paper On some decompositions of matrices over algebraically closed and finite fields
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2021
\vol 14
\issue 5
\pages 547--553
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\crossref{https://doi.org/10.17516/1997-1397-2021-14-5-547-553}
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Linking options:
https://www.mathnet.ru/eng/jsfu939
https://www.mathnet.ru/eng/jsfu/v14/i5/p547
This publication is cited in the following 2 articles:
Peter Danchev, Esther García, Miguel Gómez Lozano, “Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence”, Linear Algebra and its Applications, 676 (2023), 44
Peter Danchev, Esther García, Miguel Gómez Lozano, “Decompositions of matrices into potent and square-zero matrices”, Int. J. Algebra Comput., 32:02 (2022), 251
Citation in format AMSBIB
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