两个参数的矩阵值函数的 SVD、联合-MVD、贝里相位和一般秩损失

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-29 DOI:10.1016/j.laa.2024.07.021

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引用次数: 0

摘要

在这项研究中，我们考虑了取决于两个参数的复值矩阵函数的一般秩损失。我们给出的理论结果描述了发生秩损失的参数区域。我们的主要结果表明，在沿闭合环路进行适当的平滑 SVD 后，可以监测奇异向量累积的贝里相位，以确定在环路内部是否存在发生秩损失的参数值。这需要使用一种新的平滑 SVD 结构，我们称之为 "联合-MVD"（最小变异分解）。

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SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters

In this work we consider generic losses of rank for complex valued matrix functions depending on two parameters. We give theoretical results that characterize parameter regions where these losses of rank occur. Our main results consist in showing how following an appropriate smooth SVD along a closed loop it is possible to monitor the Berry phases accrued by the singular vectors to decide if –inside the loop– there are parameter values where a loss of rank takes place. It will be needed to use a new construction of a smooth SVD, which we call the “joint-MVD” (minimum variation decomposition).

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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.