How to get the pseudo left inverse of a singular squarem atrix?
I'm rusty, but not *that* rusty here, I hope. If W (=Z*Z' in your case) is singular, it can not
have >inverse, which by
definition also mean that nothing multiply by it will produce the identity matrix (for otherwise it would have an inverse and thus nonsingular). The definition of a generalized inverse is something like: If A is a non-null matrix, and G satisfy AGA = A, then G is called a generalized inverse of A. This is not unique, but a unique one that satisfy some additional properties is the Moore-Penrose inverse.
I >don't know if this is
what ginv() in MASS returns, as I have not used it before.
Andy The inverse of a Matrix A is defined as a Matrix B such that B*A=A*B=I and not just B*A=I. But there are matrices B for singular matrices A such that B*A=I but A*B != I, therefore there exist "left-inverses" (or "right-inverses") for non-invertable matrices. Best Regards __________________________________