关于k数值半径的平行矩阵对的线性守恒

IF 1.1 3区数学 Q1 MATHEMATICS Linear Algebra and its Applications Pub Date : 2025-03-15 Epub Date: 2025-01-21 DOI:10.1016/j.laa.2025.01.019

Bojan Kuzma , Chi-Kwong Li , Edward Poon , Sushil Singla

引用次数: 0

摘要

设1≤k<；n为整数。对于某些标量μ，当|μ|=1时，如果wk(A+μB)=wk(A)+wk(B)，则两个n×n矩阵A和B相对于k数值半径wk形成平行对；如果前面的方程对μ=1成立，则它们形成TEA（三角形相等）对。我们对Mn和Hn上保留平行对或TEA对的线性双射进行了分类。除了Hn上n=2k的一些特殊映射外，这样的保存器是周等距的标量倍。

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Linear preservers of parallel matrix pairs with respect to the k-numerical radius

Let

1 \leq k < n

be integers. Two

n \times n

matrices A and B form a parallel pair with respect to the k-numerical radius

w_{k}

w_{k} (A + μ B) = w_{k} (A) + w_{k} (B)

for some scalar μ with

| μ | = 1

; they form a TEA (triangle equality attaining) pair if the preceding equation holds for

μ = 1

. We classify linear bijections on

M_{n}

and on

H_{n}

which preserve parallel pairs or TEA pairs. Such preservers are scalar multiples of

w_{k}

-isometries, except for some exceptional maps on

H_{n}

when

n = 2 k

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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.

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