Question: Let v1,... , vn and w1.......wn be two sets of linearly independent vectors in Rn. Show that all their dot products are the same, so

Let v1,... , vn and w1.......wn be two sets of linearly independent vectors in Rn. Show that all their dot products are the same, so vi ∙ vj = wi ∙ wj for all 1, 7 = 1........n, if and only if there is an orthogonal matrix Q such that w, = Q vi for all i = 1,... , n.

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