# [R] How to get the pseudo left inverse of a singular square m atrix?

Liaw, Andy andy_liaw at merck.com
Thu Aug 14 19:24:18 CEST 2003

```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
>

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