in reply to Moore-Penrose Pseudo-Inverse Matrix

My recollection (which may be in error) is that the Moore-Penrose inverse of

chas

(Update: BTW, if you have a system of equations

`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`.)Replies are listed 'Best First'. | |
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Re^2: Moore-Penrose Pseudo-Inverse Matrix
by Angharad (Pilgrim) on Aug 02, 2005 at 10:48 UTC |

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