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parallelogram law (Theorem)
Theorem 1   In an inner product space, let $ x$ and $ y$ be vectors. Then
$\displaystyle \Vert x + y \Vert ^ 2 + \Vert x - y \Vert ^2 = 2 \Vert x \Vert ^ 2 + 2 \Vert y \Vert ^ 2.$



"parallelogram law" is owned by Mathprof.
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See Also: parallelogram law, generalization of the parallelogram law


Attachments:
proof of parallelogram law (Proof) by Wkbj79
yet another proof of parallelogram law (Proof) by Mathprof
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Cross-references: vectors
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This is version 6 of parallelogram law, born on 2006-08-02, modified 2006-10-04.
Object id is 8205, canonical name is ParallelogramLaw2.
Accessed 2064 times total.

Classification:
AMS MSC: 46C05 (Functional analysis :: Inner product spaces and their generalizations, Hilbert spaces :: Hilbert and pre-Hilbert spaces: geometry and topology )
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