# Inverse of symmetric matrix M = A*At [duplicate]

Possible Duplicate:
Inverse of symmetric matrix $M = A A^\top$

I have a matrix, generated by the product of a non-square matrix with its own transpose:

M = A * A^T


I need the inverse of M, assuming det(M) != 0.

Given the nature of the matrix M, are there any specialised computational methods to find its inverse, prioritising precision over speed? Gauss-Jordan is prone to error, and I hope to find something nicer than and with comparable precision to adj(M^T)/det(M).

I've had a quick read of the Matrix Cookbook and of this page, but (at the present time of 1am) I'm struggling to see how it could help me.

In case it helps, I'm actually trying to calculate:

B = (A * A^T)^-1 * A

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## migrated from stackoverflow.comAug 15 '12 at 12:59

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## marked as duplicate by Ｊ. Ｍ., Zhen Lin, Rudy the Reindeer, Michael Greinecker♦, Jack SchmidtAug 15 '12 at 13:24

You might get lucky here, although there are more numerical analysts on mathSE than here, so I suggest you post there. –  davin Aug 15 '12 at 0:27
thanks - what/where is mathSE? –  Mark K Cowan Aug 15 '12 at 0:32

$B = \left(A A^T\right)^{-1} A = \left(A^T\right)^{-1_{L}} = \left(A^{TT} A^T \right)^{-1} * A^{TT}$