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.
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页码：1616 / 1629
页数：14
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