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parallelogram law
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(Theorem)
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Theorem 1 In an inner product space, let $x$ and $y$ be vectors. Then $$ \Vert x + y \Vert ^ 2 + \Vert x - y \Vert ^2 = 2 \Vert x \Vert ^ 2 + 2 \Vert y \Vert ^ 2.$$
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"parallelogram law" is owned by Mathprof.
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Cross-references: vectors
There are 7 references to this entry.
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 3645 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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Pending Errata and Addenda
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