Linked from

The 31 pages that link to Inner product, each with the reason it gives.

• Fourier transformRelated: The transform’s integral compares a function with oscillatory basis functions.

• Fourier seriesRelated: Integrals of products provide the projections used to calculate Fourier coefficients.

• Euclidean distanceRelated: The standard inner product determines the Euclidean norm used for distance.

• Born ruleRelated: Measurement amplitudes are inner products between states and outcome vectors.

• OrthogonalityRelated: A pair is orthogonal precisely when this function evaluates to zero.

• Orthogonal matrixRelated: Preserving inner products is equivalent to preserving lengths and angles.

• Riesz representation theoremRelated: The representing vector acts through this pairing to produce the functional's values.

• Fourier coefficientRelated: For orthogonal Fourier bases, an inner product extracts a component’s coefficient.

• Slater determinantRelated: Orbital overlaps determine the normalization and overlaps of Slater determinants.

• Parallelogram lawRelated: Expanding the squared norms with an inner product makes the identity immediate.

• Positive-definite matrixRelated: The expression xᵀAx acts as a weighted squared length when A is positive definite.

• Magnitude (mathematics)Related: An inner product induces a norm through the square root of a vector’s self-product.

• Euclidean vectorRelated: It defines the lengths and angles that make a vector space Euclidean.

• Fundamental theorem of linear algebraRelated: It provides the notion of orthogonality used by the theorem.

• Wigner's theoremRelated: Its magnitude determines the transition probabilities that the theorem requires symmetries to preserve.

• Bra–ket notationRelated: The expression ⟨φ|ψ⟩ represents an inner product.