A matrix version of the Wielandt inequality and its applications to statistics (Q1124947)
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: A matrix version of the Wielandt inequality and its applications to statistics |
scientific article; zbMATH DE number 1371430
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A matrix version of the Wielandt inequality and its applications to statistics |
scientific article; zbMATH DE number 1371430 |
Statements
A matrix version of the Wielandt inequality and its applications to statistics (English)
0 references
29 November 1999
0 references
Let \(A\) be a positive definite matrix, and let \(X\) and \(Y\) be matrices such that \(X^*Y=0\). The authors prove the inequality \[ X^* AY(Y^* AY)^-Y^*AX \leq\left({a-b \over a+b} \right)^2X^*AX, \] where \(a\) and \(b\) are the largest and smallest eigenvalues of \(A\), respectively, and \(M^-\) stands for a generalized inverse of \(M\).
0 references
Wielandt inequality
0 references
Kantorovich inequality
0 references
Cauchy-Schwarz inequality
0 references
generalized inverse
0 references
