Section
Linear Algebra
Vector spaces, linear maps, inner products, and spectral theory
Core idea
Click any term to expand its definition inline.
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Vector Spaces
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Linear Maps
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Eigentheory
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Matrix Invariants
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Inner Products and Norms
- Inner product
- Inner product space
- Bilinear form
- Orthogonality
- Norm
- Normed vector space
- Euclidean norm
- Operator norm
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Function Spaces
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Theorems
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Conjecture dependencies
- Unit sphere of a normed space
- Surjective linear isometry
- Orthonormal basis
- Closed linear subspace
- Orthogonal complement
- Orthogonal projection
- Invariant subspace of an operator
Quaternionic and Hermitian linear algebra
- Complexification
- Quaternion division algebra
- Quaternionic vector space
- Hyperhermitian form and matrix
- Moore determinant
- Mixed discriminant
Quadratic, Hermitian, and projective linear algebra
- Realification of a complex vector space
- Quadratic form
- Signature of a symmetric bilinear form
- Hermitian matrix
- Minkowski vector space
- Semilinear map
Coordinates and calculus additions
- Cross product in three-dimensional Euclidean space
- Dual basis
- Hadamard product
- Left inverse of a linear map
- Inverse matrix
- Moving frame for a family of subspaces
- Outer product
- Quadratic map over the real numbers
- Orthogonal reflection across a hyperplane
- Right inverse of a linear map
- Unit vector
Evolution-equation prerequisites
Matrix symmetry in differential equations
Torus covers and support combinatorics
- Full-rank Euclidean lattice
- Index of an integer sublattice
- Fundamental domain of a Euclidean lattice
Cones, averages and moment constraints
- Linearized inverse for squared amplitudes
- Moment pairing matrix
- Positive realization by squared amplitudes
- Vandermonde matrix