Let V1, ,Vk be mutually orthogonal vectors in Rn . Show
Chapter 6, Problem 6.66(choose chapter or problem)
Let V1, ,Vk be mutually orthogonal vectors in Rn . Show that, for any X in Rn , k j=1 (X Vj) 2 X 2 . This is known as Bessels inequality for vectors. A version for Fourier series and eigenfunction expansions will be seen in Chapter Fifteen. Hint Let Y = X k j=1(X Vj)Vj and compute Y 2 . 23
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