In the least squares method, what does $A^T A$ indicate and, similarly, the product $A ^T b$?
That is, why do we multiply both sides of the equation $Ax = b$ by $A^T$? What does it tell us?
I know the derivation, but I'm looking for an intuitive explanation of the normal equations $$ 𝐴^𝑇𝐴𝑥=𝐴^𝑇b. $$