关于奇异值的多数化的注意事项

Pub Date : 2022-01-01 DOI:10.7153/oam-2022-16-65

Jianguo Zhao

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引用次数: 0

摘要

．在这篇笔记中，我们主要研究矩阵的乘积和的多数化。首先，我们给出了以下结果:设A i, B i, X i∈M n (C) (i = 1,2，···，M)，其中X i (i = 1,2，···，M)是可逆矩阵，设h是一个在[0，+∞)上的非负递增连续函数，h(0) = 0。若f, g是[0，+∞)上的非负连续函数，且对于t∈[0，+∞)，f (t) g (t) = t，则

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Notes on majorizations for singular values

. In this note, we mainly investigate the majorizations on the products and sums of matrices. Firstly, we present the following result: Let A i , B i and X i ∈ M n ( C ) ( i = 1 , 2 , ··· , m ) with X i ( i = 1 , 2 , ··· , m ) are invertible matrices, and let h be a nonnegative increasing continuous function on [ 0 , + ∞ ) with h ( 0 ) = 0. If f , g are nonnegative continuous functions on [ 0 , + ∞ ) with f ( t ) g ( t ) = t for t ∈ [ 0 , + ∞ ) , then

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