Inequalities for Determinants and Characterization of the Trace

Сибирский математический журнал

article

A. M. Bikchentaev¹ 

[1] Lobachevskii Institute of Mathematics and Mechanics of Kazan (Volga Region) Federal University

关键词: linear functional;    matrix;    trace;    determinant;    permanent;    matrix exponential;    Fischer inequality;   

DOI  :  10.1134/S0037446620020068

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Let tr be the canonical trace on the full matrix algebra $${{\cal M}_n}$$ with unit I. We prove that if some analog of classical inequalities for the determinant and trace (or the permanent and trace) of matrices holds for a positive functional φ on $${{\cal M}_n}$$ with φ(I) = n, then φ = tr. Also, we generalize Fischer’s inequality for determinants and establish a new inequality for the trace of the matrix exponential.

【 授权许可】

CC BY