My recollection (which may be in error) is that the Moore-Penrose inverse of A
is invertible (i.e. if the columns of A
are independent.) (I'm using ^ to indicate exponenents as in TeX
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.
(Update: BTW, if you have a system of equations Ax=b
is the usual "least squares"
solution, i.e. the x
for which Ax
is closest to b
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