       Re: Inverting a non-square matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg20252] Re: [mg20201] Inverting a non-square matrix
• From: "Mark E. Harder" <harderm at ucs.orst.edu>
• Date: Fri, 8 Oct 1999 18:30:23 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Nicolas,
There is no general formula, or algorithm for inverting a general
non-square matrix, that I'm aware of.  There *may* be "left" and "right"
inverses in special cases, when the rows or columns span their column spaces
(I forget which case goes with which inverse.), but of course, you can't
tell whether the necessary conditions are met for purely symbolic
rectangular matrices, such as yours.  Even square matrices have to be
non-singular to have an inverse.  If the rectangular matrix is numerical,
not symbolic, then one can calculate a "pseudoinverse", which is useful in
finding least-squares approximations to overdetermined and underdetermined
linear systems -- see a good book on numerical linear algebra for a
discussion of this.
-mark

Subject: [mg20252] [mg20201] Inverting a non-square matrix

>Hi all,
>
>I learnt a bit of Mathematica when I was student and I need a formal
>calculation of the inverse of a non square matrix. But we do not have
>the software in my department.
>Can anyone say me if it is possible, and what are the formulas?
>My matrix is:
>A =
>[a b c d]
>[e f g h]
>[i j k l]
>and all the parameters are variable.
>