On a number of previous occasions, I have used the pseudoinverse of a matrix solve systems of equations, and do other things such as channel mixing. However, the demonstration I gave before isn’t entirely correct. Let’s see now why it’s important to make the difference between a left and a right pseudoinverse.
I always disliked when a book gives equations and formulas as if of fiat without providing justification or demonstration; and I don’t mind that they skip a few steps as long that I can fill in the blanks myself if I care to. Linear regression is one of those formula we see but we’d like to understand better.
So let us see how to derive the formulas for linear regression and see how they generalize to any number of unknowns.