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Exercise 6.4.15

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Let $T = L_{A}$ and $U = L_{B}$ . Applying the previous exercise, we find some orthonormal basis $β$ such that ${[T]}_{β}$ and ${[U]}_{β}$ are diagonal. Denote $α$ to be the standard basis. Now we have that

{[T]}_{β} = {[I]}_{α}^{β} A {[I]}_{β}^{α}

and

{[U]}_{β} = {[I]}_{α}^{β} B {[I]}_{β}^{α}

are diagonal. Pick $P = {[I]}_{β}^{α}$ and get the desired result.

jephianlin

2011-06-27 00:00

Exercise 6.4.15

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