This is a homework problem i had. Help!
Explain why the dot product of x and y equals the dot product of Px and Py.
Then From (Px)^T(Py)=x^Ty deduce that P^TP=I for any permutation. With x=(1,2,3) and y=(1,4,20) choose P to show that Pxdoty is not always xdotPy.