On Inner Products in Linear, Metric Spaces¶
Jordan, P., & Neumann, J. v. (1935). On Inner Products in Linear, Metric Spaces. Annals of Mathematics, 36(3), 719-723.
Cited by¶
1 citation across 1 artifact.
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Domain-specific¶
- Parallelogram Law
- Jordan and von Neumann proved the characterizing result in 1935: over the real or complex scalars, a norm satisfies the parallelogram law for all vector pairs if and only if there is an inner product whose induced norm is the given norm.
This sourceInstitutional copy: <https://www.mathematik.uni-muenchen.de/~michel/jordan-von_neumann_-_parallelogram_identity.pdf>. Verified 2026-08-26.
- Jordan and von Neumann proved the characterizing result in 1935: over the real or complex scalars, a norm satisfies the parallelogram law for all vector pairs if and only if there is an inner product whose induced norm is the given norm.
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