[unishark]

A little defense of the pseudoinverse here, it's often a fine tool, far more so than the true inverse.

If the matrix is not full rank the psuedoinverse provides the least squares solution.

It can also be done efficiently and may well already be implemented using whatever numerical method one prefers (SVD, QR).

And the implementation probably allows for regularization via a singular value cutoff.

I'm not sure what matlab's backslash operator does these days, but it looks like a more efficient way to get a least-squares solution (compared to the pseudoinverse), possibly with sparsity imposed slightly.