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
-----Original Message----- From: Feng Zhang [mailto:f0z6305 at labs.tamu.edu] Sent: Thursday, August 14, 2003 1:02 PM To: Jerome Asselin; R-Help Subject: Re: [R] How to get the pseudo left inverse of a singular square matrix? Thank, Jerome The question is if this generalized inverse can make their product to be identity matrix? ----- Original Message ----- From: "Jerome Asselin" <jerome at hivnet.ubc.ca> To: "Feng Zhang" <f0z6305 at labs.tamu.edu>; "R-Help" <r-help at stat.math.ethz.ch> Sent: Thursday, August 14, 2003 11:52 AM Subject: Re: [R] How to get the pseudo left inverse of a singular square matrix?
Singular matrices are not invertible. However you can calculate the generalized inverse with the function ginv() from package MASS. HTH, Jerome On August 14, 2003 09:24 am, Feng Zhang wrote:
Dear R-listers, I have a dxr matrix Z, where d > r. And the product Z*Z' is a singular square matrix. The problem is how to get the left inverse U of this
singular matrix
Z*Z', such that U*(Z*Z') = I? Is there any to figure it out using matrix decomposition method? Thanks a lot for your help. Fred
______________________________________________ R-help at stat.math.ethz.ch mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
______________________________________________ R-help at stat.math.ethz.ch mailing list https://www.stat.math.ethz.ch/mailman/listinfo> /r-help
------------------------------------------------------------------------------ Notice: This e-mail message, together with any attachments, contains information of Merck & Co., Inc. (Whitehouse Station, New Jersey, USA), and/or its affiliates (which may be known outside the United States as Merck Frosst, Merck Sharp & Dohme or MSD) that may be confidential, proprietary copyrighted and/or legally privileged, and is intended solely for the use of the individual or entity named on this message. If you are not the intended recipient, and have received this message in error, please immediately return this by e-mail and then delete it.