21. Orthonormal Bases
Then as a linear transformation, P i w iw T i = I n xes every vector, and thus must be the identity I n. De nition A matrix Pis orthogonal if P 1 = PT. Then to summarize, Theorem. A change of basis matrix P relating two orthonormal bases is an orthogonal matrix. i.e. P 1 = PT: Example Consider R3 with the orthonormal basis S= 8 >> < >>: u 1 = 0 ...
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