COUPLED SYLVESTER-TYPE MATRIX EQUATIONS AND BLOCK DIAGONALIZATION

被引：69

作者：

Dmytryshyn, Andrii ^{[1
,2
]}

Kagstrom, Bo ^{[1
,2
]}

机构：

[1] Umea Univ, Dept Comp Sci, SE-90187 Umea, Sweden

[2] Umea Univ, HPC2N, SE-90187 Umea, Sweden

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2015年 / 36卷 / 02期

基金：

瑞典研究理事会;

关键词：

matrix equation; Sylvester equation; Stein equation; Roth's theorem; consistency; block diagonalization; SOLVING TRIANGULAR SYSTEMS; PENCILS CODIMENSION COUNTS; GENERALIZED SYLVESTER; ROTH THEOREMS; CONSISTENCY; ALGORITHMS; PAIR; SUBSPACES;

D O I：

10.1137/151005907

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove Roth-type theorems for systems of matrix equations including an arbitrary mix of Sylvester and star-Sylvester equations, in which the transpose or conjugate transpose of the unknown matrices also appear. In full generality, we derive consistency conditions by proving that such a system has a solution if and only if the associated set of 2 x 2 block matrix representations of the equations are block diagonalizable by (linked) equivalence transformations. Various applications leading to several particular cases have already been investigated in the literature, some recently and some long ago. Solvability of these cases follow immediately from our general consistency theory. We also show how to apply our main result to systems of Stein-type matrix equations.

引用

页码：580 / 593

页数：14

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