SOLVING THE PROBLEM OF SIMULTANEOUS DIAGONALIZATION OF COMPLEX SYMMETRIC MATRICES VIA CONGRUENCE

被引：7

作者：

Bustamante, Miguel D. ^{[1
]}

Mellon, Pauline ^{[1
]}

Velasco, M. Victoria ^{[2
]}

机构：

[1] Univ Coll Dublin, Sch Math & Stat, Dublin 4, Ireland

[2] Univ Granada, Fac Ciencias, Dept Anal Matemat, Granada 18071, Spain

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2020年 / 41卷 / 04期

关键词：

simultaneous diagonalization by congruence; simultaneous diagonalization by similarity; linear pencil; BLIND SOURCE SEPARATION; JOINT DIAGONALIZATION; PAIRS;

D O I：

10.1137/19M1280430

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a solution to the problem of simultaneous diagonalization via congruence of a given set of m complex symmetric n x n matrices {A(1), ..., A(m)}, by showing that it can be reduced to a possibly lower-dimensional problem where the question is rephrased in terms of the classical problem of simultaneous diagonalization via similarity of a new related set of matrices. We provide a procedure to determine in a finite number of steps whether or not a set of matrices is simultaneously diagonalizable by congruence. This solves a long-standing problem in the complex case.

引用

页码：1616 / 1629

页数：14

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