PreprintCC BY 4.0arXiv
Linear maps preserving the matrix discriminant. An enhanced approach
Abstract
The discriminant of a square matrix is defined as a discriminant of its characteristic polynomial. In this paper we provide a description of linear maps preserving the matrix discriminant assuming that the ground field is large enough. Our description generalizes the known results to the case where the field may have a finite cardinality and its characteristic may divide the size of considered matrices. To obtain this description, we extend the approach used in our previous work on the subject and, in addition to that, introduce new invariants for the action of all bijective linear maps preserving a given polynomial, which are on independent interest and could be applied to other problems in the theory of linear preservers.
Related
- Linear Rank Nonincreasing and Preserving Maps between Matrix Spaces
- Linear maps preserving the Cullis' determinant. III
- Linear maps preserving families of C-symmetric operators
- Linear maps of C*-algebras preserving norm parallelism
- Linear maps preserving Kasparov cycles and the characterization of induced automorphisms
BibTeX
@misc{yurkov2026linear,
title = {{Linear maps preserving the matrix discriminant. An enhanced approach}},
author = {Andrey Yurkov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14060},
eprint = {2610.14060},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14060},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linear maps preserving the matrix discriminant. An enhanced approach
AU - Andrey Yurkov
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.14060
UR - https://arxiv.org/abs/2610.14060
AB - The discriminant of a square matrix is defined as a discriminant of its characteristic polynomial. In this paper we provide a description of linear maps preserving the matrix discriminant assuming that the ground field is large enough. Our description generalizes the known results to the case where the field may have a finite cardinality and its characteristic may divide the size of considered matrices. To obtain this description, we extend the approach used in our previous work on the subject and, in addition to that, introduce new invariants for the action of all bijective linear maps preserving a given polynomial, which are on independent interest and could be applied to other problems in the theory of linear preservers.
ER -