Linear Bijective Maps Sending Nilpotent Matrices into Matrices of Local Spectral Radius Zero at a Fixed Vector
Year: 2026
Type: article
Abstract: For a natural number n , denote by $$\mathcal {M}_n$$ M n the algebra of all matrices of size n over the complex field $$\mathbb {C}$$ C . Let also $$x_0$$ x 0 be a fixed nonzero vector in $$\mathbb {C}^{n}$$ C n . In this paper, we characterize linear bijective maps on $$\mathcal {M}_n$$ M n sending nilpotent matrices into matrices of local spectral radius zero at $$x_0$$ x 0 . As a corollary, we also give the general form of linear bijective maps on $$\mathcal {M}_n$$ M n sending matrices of local spectral radius zero at $$x_0$$ x 0 into matrices of the same type.
Source: Results in Mathematics
Author: Constantin COSTARA
Institution: Ovidius University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7165205122