※ 引述《ihtfjxj28 (阿斌)》之銘言:
:
: ∣ x ∣ ∣ cosθ -sinθ ∣ ∣ u ∣
: ∣ y ∣=∣ sinθ cosθ ∣ ∣ v ∣
let {A} = (x, y); {B} = (u, v);
[Q] = (cosθ -sinθ,sinθ cosθ)
-> {A} = [Q]{B}
if [Q] have inv[Q], {B} = inv[Q]{A}
because [Q] is orthonormality, inv[Q] = tr[Q]
-> {A} = tr[Q]{B}
: ∣ u ∣ ∣ cosθ sinθ ∣ ∣ x ∣
: ∣ v ∣=∣-sinθ cosθ ∣ ∣ y ∣
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