Rank Function Equations and their solution sets
Piotr Pokora
TL;DR
This paper investigates solutions to rank function equations, focusing on non-nilpotent matrices and exploring geometric properties of solution sets in the nilpotent case.
Contribution
It introduces new insights into the structure of solutions to rank function equations and explores their geometric properties, especially for nilpotent matrices.
Findings
Characterization of solutions for non-nilpotent matrices
Geometric properties of solution sets in the nilpotent case
New theoretical insights into rank function equations
Abstract
We examine so-called rank function equations and their solutions consisting of non-nilpotent matrices. Secondly, we present some geometrical properties of the set of solutions to certain rank function equations in the nilpotent case.
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