[beagle3]

The reason you want to avoid matrix inversion is not computational performance - it is precision.

You can generally "multiply by the inverse" without actually computing the inverse, in a way that needs less intermediate floating point precision.

If your matrices have a large spread of eigenvalues, it makes a lot of difference - double precision often doesn't have enough precision for direct inversion in the real world.

(And even if you do want to invert, it is more numerically stable to do that as a solution of Ax=e, for each 'e' a basis element, as long as you compute A^-1 \* e indirectly using a numerically stable method)

[rohitarondekar]

Thank you for explaining, I think I get it now. The ML course on Coursera is a little light on the Maths. As in the professor only explains as much is needed to perform the techniques. So I think I'll be watching Strangs Linear Algebra lectures on OCW soon. :)