Let W V with dim V = n. Suppose w1........wn, is an orthogonal basis for W
Question:
(a) Prove that the combination w1,...,wn forms an orthogonal basis of V.
(b) Show that if v = c1w1 + ... cn wn is any vector in V, then its orthogonal decomposition v = w + z is given by w = c1 w1 + ... + cm wm ∊ W and z = cm+1 wm+1 + ... + cn wn ∊ W⊥.
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a We are given that w i w j 0 for all i j between 1 and m and between m 1 and n It is also ...View the full answer
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