Question: Let (V, ) be an inner product space, w V - {0} and W = span{w} be a line. If P: V W is

Let (V, ) be an inner product space, w V - {0}

Let (V, ) be an inner product space, w V - {0} and W = span{w} be a line. If P: V W is a non-zero linear transformation such that P2 = P and < Px,y >= < x, Py >, show that P is the orthogonal projection, i.e., for all v V, P(v) = = w.

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ANSWER To show that P is the orthogonal projection onto W we need to show two things first that Pv i... View full answer

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