Question: Let v be a vector in an inner product space V. (a) Show that ||v|| > ||projU(v)|| holds for all finite dimensional subspaces U. [Hint:

Let v be a vector in an inner product space V.
(a) Show that ||v|| > ||projU(v)|| holds for all finite dimensional subspaces U.
[Hint: Pythagoras' theorem.]
If {e1,e2,..., ew} is any orthogonal set in V, prove Bessel's inequality:

v, e ei ew

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