Prove that the change of basis matrix from one orthonormal basis of to another is always orthogonal.

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- Nov 3rd 2010, 09:16 PMdavesfaceChange of basis matrices
Prove that the change of basis matrix from one orthonormal basis of to another is always orthogonal.

- Nov 4th 2010, 05:05 AMHallsofIvy
If and are bases for the same vector space, then A is the "change of basis matrix" if and only if and . If is an orthonormal basis then where is the "Kronecker delta", equal to 1 if i= j, 0 otherwise.