On the Sensitivity of the Canonical Angles of a Unitoid Matrix

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2022-12-08 DOI:10.1134/s199542392204005x

Kh. D. Ikramov, A. M. Nazari

引用次数: 0

Abstract

A unitoid matrix is a square complex matrix that can be brought to diagonal form by a Hermitian congruence transformation. The canonical angles of a nonsingular unitoid matrix \(A\) are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of \(A\), which is the matrix \(A^{-*}A\). We derive an estimate for the derivative of an eigenvalue of the cosquare in the direction of the perturbation in \(A^{-*}A\) caused by a perturbation in \(A\).

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论酉阵正则角的灵敏度

一元矩阵是一种可以通过厄米同余变换转化为对角形式的平方复矩阵。非奇异单位阵\(A\)的规范角是(直到因子1/2)\(A\)的余方的特征值的参数，也就是矩阵\(A^{-*}A\)。我们导出了由\(A\)中的扰动引起的\(A^{-*}A\)中扰动方向上的余方特征值的导数的估计。

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

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.