Some interlacing properties of the Schur complement of a Hermitian matrix (Q1208267)
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: Some interlacing properties of the Schur complement of a Hermitian matrix |
scientific article; zbMATH DE number 166220
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some interlacing properties of the Schur complement of a Hermitian matrix |
scientific article; zbMATH DE number 166220 |
Statements
Some interlacing properties of the Schur complement of a Hermitian matrix (English)
0 references
16 May 1993
0 references
The author presents the following result: --- It is shown for a Hermitian matrix \(H\) with nonsingular principal submatrix \(A\), that the eigenvalues of the Moore-Penrose inverse of the Schur complement \((H/A)\) of \(A\) in \(H\) interlace the eigenvalues of the Moore-Penrose inverse of \(H\). Also, if \(H\) is semidefinite, then the eigenvalues of \((H/A)\) interlace the eigenvalues of \(H\).
0 references
Hermitian matrix
0 references
eigenvalues
0 references
Moore-Penrose inverse
0 references
Schur complement
0 references
