List of linear algebra topics

This is a list of linear algebra topics. See also:

List of matrices
Glossary of tensor theory.

Linear equations

System of linear equations
Determinant
- Minor
- Cauchy–Binet formula
Cramer's rule
Gaussian elimination
Gauss–Jordan elimination
Strassen algorithm

Matrices

2 × 2 real matrices
Matrix theory
Matrix addition
Matrix multiplication
Basis transformation matrix
Characteristic polynomial
Trace
Eigenvalue, eigenvector and eigenspace
Rank
Matrix inversion, invertible matrix
- Pseudoinverse
Adjugate
Transpose
- Dot product
- Symmetric matrix
- Orthogonal matrix
- Skew-symmetric matrix
- Conjugate transpose
  - Unitary matrix
  - Hermitian matrix, Antihermitian matrix
Positive-definite, positive-semidefinite matrix
Pfaffian
Projection
Spectral theorem
Perron–Frobenius theorem
List of matrices

Matrix decompositions

Relations

Computations

Vector spaces

Linear combination
Linear span
Linear independence
Scalar multiplication
Basis
- Change of basis
- Hamel basis
Cyclic decomposition theorem
Dimension theorem for vector spaces
- Hamel dimension
Examples of vector spaces
Linear map
- Shear mapping or Galilean transformation
- Squeeze mapping or Lorentz transformation
Linear subspace
- Row and column spaces
- Column space
- Row space
- Cyclic subspace
- Null space, nullity
- Rank–nullity theorem
- Nullity theorem
Dual space
- Linear function
- Linear functional
Category of vector spaces

Structures

Topological vector space
Normed vector space
Inner product space
- Euclidean space
- Orthogonality
- Orthogonal complement
- Orthogonal projection
- Orthogonal group
Pseudo-Euclidean space
- Null vector
- Indefinite orthogonal group
Orientation (geometry)
- Improper rotation
Symplectic structure

Multilinear algebra

Tensor
- Classical treatment of tensors
- Component-free treatment of tensors
Outer product
Tensor algebra

Affine space and related topics

Projective space

Linear algebra
Basic concepts	Scalar Vector Vector space Scalar multiplication Vector projection Linear span Linear map Linear projection Linear independence Linear combination Basis Change of basis Row and column vectors Row and column spaces Orthogonality Kernel Eigenvalues and eigenvectors Outer product Inner product space Dot product Transpose Gram–Schmidt process Linear equations
Vector algebra	Cross product Triple product Seven-dimensional cross product
Multilinear algebra	Geometric algebra Exterior algebra Bivector Multivector Tensor Outermorphism
Matrices	Block Decomposition Invertible Minor Multiplication Rank Transformation Cramer's rule Gaussian elimination Determinant
Algebraic constructions	Dual Direct sum Function space Quotient Subspace Tensor product
Numerical	Floating-point Numerical stability Basic Linear Algebra Subprograms (BLAS) Sparse matrix Comparison of linear algebra libraries Comparison of numerical analysis software
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