What does the 'Hat Matrix' H=X(XTX)−1XTH = X(X^T X)^{-1} X^TH=X(XTX)−1XT satisfy?
It is symmetric and idempotent (H2=HH^2 = HH2=H).
Its determinant is always 1.
Its trace is always equal to nnn.
It is always a diagonal matrix.