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Exercise 6.9.2

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We already have that

⟨ T_{v}^{∗} L_{A} T_{v} (w), w ⟩ = 0

if $⟨ L_{A} (w), w ⟩ = 0$ for $w \in ℝ^{4}$ whose fourth entry is nonnegative. Now if we have $⟨ L_{A} (w), w ⟩ = 0$ for some $w$ is a vector in $ℝ^{4}$ whose fourth entry is negative, then we have

0 = ⟨ T_{v}^{∗} L_{A} T_{v} (- w), - w ⟩ = {(- 1)}^{2} ⟨ T_{v}^{∗} L_{A} T_{v} (w), w ⟩ = ⟨ T_{v}^{∗} L_{A} T_{v} (w), w ⟩ .

jephianlin

2011-06-27 00:00

Exercise 6.9.2

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