On scaled projections and pseudoinverses
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 \(\| X^+_ D\| \leq c\| X^+\|\).
scientific article; zbMATH DE number 4075275