On scaled projections and pseudoinverses (Q1111643)
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scientific article; zbMATH DE number 4075275
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On scaled projections and pseudoinverses |
scientific article; zbMATH DE number 4075275 |
Statements
On scaled projections and pseudoinverses (English)
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1989
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Let X be a matrix of full column rank and let D be a diagonal matrix with positive diagonal elements. The weighted pseudoinverse of X is defined by \(X^+_ D=(X^ tDX)^{-1}X^ tD\) and the associated oblique projection is defined by \(P_ D=XX^+_ D\). The author proves that there is a positive number c which is independent of D such that \(\| P_ D\| \leq c\) and \(\| X^+_ D\| \leq c\| X^+\|\).
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norm of matrix
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weighted pseudoinverse
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