Projection operator

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

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

Or p=x^=P^b=[aTb/(aTa)]ap = \hat x = \hat Pb = [a^Tb / (a^Ta)]a

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