Inversion of rectangular complex valued matrix

Inversion of rectangular complex valued matrix - Messages

#1 Posted: 5/20/2010 10:34:14 AM
ofniw

ofniw

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Hi,

Many thanks to Andrey and the team for SMath Studio. You did a wonderful job.

I would like to add to the box of ideas an additional request. Let me explain the background.

When having mathematical problems which include solving of linear least squares proplems, like
y=A*x
where A is a complex valued matrix, x and y are complex valued vectors. A and y is known and the objective is to find a solution for x. Normaly the system is overdetermined then A is not a square matrix. The solution normaly given is
x=(AT*A)^-1 * AT * y
where AT is the complex conjugate of the transpose of A. (AT*A^) is a square matrix and can be inverted. However this solution is known as being sensitive to a bad conditoned matrix A. Unfortunately in practice this is often the case. With e.g. Matlab, there is a function called "pinv", which inverts non square matrices using a singular value decomposition (SVD) to achieve a numerically stable result.

I would think, having the SVD and the pinv could greatly enhance the possibilities of the Smath software in the direction of linear algebra.

Please comment.
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