Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem

IF 0.8 4区 数学 Q2 Mathematics
N. T. Son, T. Stykel
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引用次数: 7

Abstract

Symplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the trace minimization theorem, have been extended to the case of symplectic eigenvalues. In this note, we will generalize Williamson's diagonal form for symmetric positive-definite matrices to the case of symmetric positive-semidefinite matrices, which allows us to define symplectic eigenvalues, and prove the trace minimization theorem in the new setting.
半正定矩阵的辛特征值与迹极小化定理
辛特征值通常是通过Williamson对角线形式定义对称正定矩阵的。许多标准特征值的性质,包括迹极小定理,已经推广到辛特征值的情况。本文将对称正定矩阵的Williamson对角线形式推广到对称正定矩阵的情况,使我们能够定义辛特征值,并证明了在这种新情况下的迹极小定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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