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### Re: Moore-Penrose Pseudo-Inverse Matrix

by chas (Priest)
 on Aug 01, 2005 at 20:11 UTC ( #480020=note: print w/replies, xml ) Need Help??

in reply to Moore-Penrose Pseudo-Inverse Matrix

My recollection (which may be in error) is that the Moore-Penrose inverse of A is: (A^tA)^{-1}A^t which exists if A^tA is invertible (i.e. if the columns of A are independent.) (I'm using ^ to indicate exponenents as in TeX source.) A^tA is square, and there are many existing routines to invert a square matrix - I'm sure there are some Perl modules that do this, although you could write your own as an exercise. You indicate above that A and the M-P inverse are symmetric, but I don't believe this is correct. The point of the M-P inverse is that it can be applied to non-square matrices.
chas
(Update: BTW, if you have a system of equations Ax=b then x=(A^tA)^{-1}A^tb is the usual "least squares" solution, i.e. the x for which Ax is closest to b.)

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Re^2: Moore-Penrose Pseudo-Inverse Matrix
by Angharad (Pilgrim) on Aug 02, 2005 at 10:48 UTC
Thanks for the suggestions :)

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