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generalization of the parallelogram law (Theorem)
Theorem 1   In an inner product space, let $x,y,z$ be vectors. Then $$ \Vert x+y\Vert^2 + \Vert y +z \Vert^2 + \Vert z +x \Vert^2 = \Vert x \Vert^2 + \Vert y \Vert^2 + \Vert z \Vert^2 + \Vert x + y +z \Vert^2. $$

Taking $x+z=0$ we have the usual parallelogram law.



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


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proof of generalization of the parallelogram law (Proof) by Mathprof
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Cross-references: parallelogram law, vectors

This is version 7 of generalization of the parallelogram law, born on 2006-08-06, modified 2006-11-27.
Object id is 8227, canonical name is GeneralizationOfTheParallelogramLaw.
Accessed 1310 times total.

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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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