Linked from

The 14 pages that link to Inner product space, each with the reason it gives.

• Hilbert spaceNarrower topic: A Hilbert space is an inner product space that also satisfies completeness.

• Vector spaceBroader topic: An inner product adds notions of orthogonality and length absent from bare vector spaces.

• Euclidean spaceNarrower topic: A positive-definite inner product on displacements provides the Euclidean metric.

• Fourier analysisNarrower topic: Fourier coefficients arise from projections in spaces of functions.

• Normed vector spaceCompared with: An inner product gives angle information that a general norm need not provide.

• OrthogonalityNarrower topic: Orthogonality is defined by the inner product that equips this space.

• Singular value decompositionRelated: Orthogonality and length underlie the singular vectors and unitary factors.

• Orthogonal projectionNarrower topic: Orthogonality and distance depend on this structure.

• Harmonic analysisNarrower topic: It supplies the geometry behind projection onto oscillatory components.

• Spectral theoremNarrower topic: Orthonormal eigenvectors are defined using its geometry.

• Geometric algebraRelated: Its metric information determines how vectors multiply geometrically.

• Bessel's inequalityNarrower topic: Bessel’s inequality is formulated through the inner products and norms of this structure.

• Parseval's identityNarrower topic: The identity follows from preservation of inner products under a complete orthonormal expansion.

• Parseval's theoremNarrower topic: Parseval’s theorem is an inner-product preservation statement in Fourier coordinates.