Linear Least Squares - Stanford University

simple properties of the hat matrix are important in interpreting least squares. By writing H 2= HHout fully and cancelling we nd H = H. A matrix Hwith H2 = His called idempotent. In hindsight, it is geometrically obvious that we should have had H2 = H. For any y2Rnthe closest point to yinside of Mis Hy. Since Hyis already in M, H(Hy) = Hy. That is H2y= Hyfor any yand so H2 = H. Clearly Hk ... ................
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