Preserver problems on Toeplitz matrices
Rayhan Ahmed, Vladimir Bolotnikov, William Hoyle, Chi-Kwong Li
TL;DR
This paper investigates linear preserver problems on Toeplitz matrices, providing characterizations for preservers of rank one matrices and determinants, and exploring related questions on structured matrices.
Contribution
It offers new characterizations of linear preservers on Toeplitz matrices, focusing on rank one and determinant preservers, advancing understanding of structured matrix preservers.
Findings
Characterization of linear preservers of rank one Toeplitz matrices
Characterization of linear preservers of the determinant on Toeplitz matrices
Discussion of related problems on other structured matrices
Abstract
We study linear preserver problems on the linear space of Toeplitz matrices over the real field or the complex field. In particular, characterizations are given for linear preservers of rank one matrices and linear preservers of the determinant. We also present related results and questions on other structured matrices.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Holomorphic and Operator Theory