A sesquilinear form ⟨·,·⟩: V×V → F satisfying conjugate symmetry, linearity in first slot, positive-definiteness. Induces a norm ||v|| = √⟨v,v⟩.
Inner product
Related concepts
- Vector space
- Orthogonality
- Spectral theorem
- Positive-definite matrix
- Lp space
- Vector space
- Hilbert space
- Riemannian metric
- Cauchy–Schwarz inequality
- Quadratic form
- Supporting hyperplane + Hahn-Banach separation of convex sets
- Hilbert space (physics use)
- Baroclinic instability: σ ~ U·f/(H·N)
- Mahalanobis d² = (x−μ)ᵀΣ⁻¹(x−μ): covariance-respecting distance metric
- Frontier molecular orbital theory
- [4+2] Diels-Alder: aromatic 6π transition state (thermally allowed, Woodward-Hoffmann)