When we use linear regressition, we have to inverse a matrix that depend on our dessign matrix, but it could happen that this matrix is not intersible. If your are using a library it handles it using a pseudoinverse. But there are families of inverses that can be choosen, in this paper I will develop rigirously to the most important ones and why pseudoinverse is the optimal option, in therms of computation and interpretation of the linear regression.
Assigment of Mathematical Statistics class.