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CG-Basics-01-Math - KDD

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... Proof. If x ∈ S1 ⊕ S2 then by definition there exist s1 ∈ S1 , s2 ∈ S2 such that x = s1 + s2 . Assume x = s01 + s02 , s01 ∈ S1 , s02 ∈ S2 , then s1 − s01 = s2 − s02 . This implies that s1 − s01 and s2 − s02 are in S1 and also in S2 . However, S1 ∩ S2 = {0}, so we conclude s1 = s01 and s2 = s02 . We ...
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the full course notes are available here in book form for downloading

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Laplace–Runge–Lenz vector

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