三个矩形矩阵Böttcher-Wenzel不等式的推广

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-07-08 DOI:10.1016/j.laa.2025.07.005

Motoyuki Nobori

引用次数: 0

摘要

设m n为正整数。对于所有m×n复矩阵A，C和一个n×m矩阵B，我们定义了一个广义对易子ABC−CBA。我们估计它的Frobenius范数，最后得到不等式，它是Böttcher-Wenzel不等式的推广。如果n=1或m=1，则ABC−CBA的Frobenius范数可以用更紧的上界估计。

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A generalization of the Böttcher-Wenzel inequality for three rectangular matrices

Let

m, n

be positive integers. For all

m \times n

complex matrices

A, C

and an

n \times m

matrix B, we define a generalized commutator as

A B C - C B A

. We estimate the Frobenius norm of it, and finally get the inequality, which is a generalization of the Böttcher-Wenzel inequality. If

n = 1

m = 1

, then the Frobenius norm of

A B C - C B A

can be estimated with a tighter upper bound.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.