Find an inner product such that the vectors ( −1, 2 )T and ( 1, 2 )T form an orthonormal basis of R2
2
4.1.11. Prove that every orthonormal basis of R2 under the standard dot product has the form u1 =
cos θ
sin θ
and u2 = ±
− sin θ
cos θ
for some 0 ≤ θ < 2π and some choice of ± sign.
.
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