Projection operator

The projection operator $\hat P$ for a vector is

$\hat P = \frac{aa^T}{a^Ta}$

Or $p = \hat x = \hat Pb = [a^Tb / (a^Ta)]a$

⇒ Generally, if the set of column vectors $\{a_i\}$ of $A$ is all orthogonal we have least-square fitting.