I dare say that you have most of us at a disadvantage.
I for one have absolutely no idea what that question means.
You must define the terms and explain the notation.
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.
P is a "permutation" matrix: every row and column contains exactly one "1" and all other entries are 0. For example,
just permutes the entries x, y, and z.
If, instead of we use then .
Essentially since both x and v are permuted in the same way, the "corresponding terms" still match up.
However,
while
so is not, in general, equal to .