Pseudo-inverse of a matrix (Moore-Penrose)

The Moore-Penrose pseudo-inverse provides the least-squares solution to problems of the form , even if the matrix is non-invertible or non-square. Because it can be implemented using singular value composition, it requires fewer operations than matrix inversion, which requires calculating the determinant.

The pseudo-inverse is defined as

There is an elegant derivation in Chaudhury 2024, ch. 2 (linear algebra).