On Hermitian nonnegative-definite solutions to matrix equations (Q1033949)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On Hermitian nonnegative-definite solutions to matrix equations |
scientific article; zbMATH DE number 5628174
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Hermitian nonnegative-definite solutions to matrix equations |
scientific article; zbMATH DE number 5628174 |
Statements
On Hermitian nonnegative-definite solutions to matrix equations (English)
0 references
10 November 2009
0 references
The authors consider the system of \(q\) matrix equations \(A_iXA_i^*=B_iB_i^*\), \(1\leq i\leq q\) and the existence of Hermitian nonnegative-definite solutions (HNNDSs). To a result obtained by \textit{X. Zhang} [J. Multivariate Anal. 93, No.~2, 257--266 (2005; Zbl 1071.15014)] (necessary and sufficient conditions for the existence of HNNDSs with \(q=2\)) they propose an alternative with simplification and regularity. They give a necessary condition for the general case and formulate a conjecture which agrees with at least one of the special situations.
0 references
matrix equation
0 references
Hermitian nonnegative-definite solution
0 references
Hermitian matrix
0 references
Moore-Penrose inverse
0 references
0 references
