I have a matrix, generated by the product of a non-square matrix with its own transpose:
$$M = A A^\top.$$
I need the inverse of $M$, assuming $\det(M) \neq 0$.
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 the adj/det method.
$M$ will either have be around $70 \times 70$, or $1000 \times 1000$ in size.
I've had a quick read of the Matrix Cookbook and of this page, but (at the present time of 1 am) I'm struggling to see how it could help me.
In case it helps, I'm actually trying to calculate:
$$B = (A A^\top)^{-1} A.$$