On maps preserving square roots of idempotent and rank-one nilpotent matrices

Autor:	Nikita Borisov, Hayden Julius, Martha Sikora
Rok vydání:	2021
Předmět:	Combinatorics Nilpotent Algebra and Number Theory Square root Rank (linear algebra) Direct sum Applied Mathematics Idempotence Bijection Idempotent matrix Nilpotent matrix Mathematics
Zdroj:	Journal of Algebra and Its Applications. 21
ISSN:	1793-6829 0219-4988
DOI:	10.1142/s0219498822501237
Popis:	We characterize bijective linear maps on [Formula: see text] that preserve the square roots of an idempotent matrix (of any rank). Every such map can be presented as a direct sum of a map preserving involutions and a map preserving square-zero matrices. Next, we consider bijective linear maps that preserve the square roots of a rank-one nilpotent matrix. These maps do not have standard forms when compared to similar linear preserver problems.
Databáze:	OpenAIRE
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