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LosTacos
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Homework Statement
Let B be an ordered orthonormal basis for a k-dimensional subspace V of ℝn. Prove that for all v1,v2 ∈ V, v1·v2 = [v1]B · [v2]B, where the first dot product takes place in ℝn and the second takes place in ℝk.
Homework Equations
The Attempt at a Solution
Let B = (b1,...,bk)
Express v1 and v2 as linear combinations of the vectors in B:
v1 = a1v1 + a2v2 + ... + akvk
v2 = b1v1 + b2v2 + ... + bkvk
I am confused as to where to go from here.