Outline of linear algebra
Linear equations
Linear equation- System of [linear equations]
- Determinant
- *Minor
- *Cauchy–Binet formula
- Cramer's rule
- Gaussian elimination
- Gauss–Jordan elimination
- Overcompleteness
- Strassen algorithm
Matrices
Matrix- Matrix addition
- Matrix multiplication
- Basis transformation matrix
- Characteristic polynomial
- Trace
- Eigenvalue, eigenvector and eigenspace
- *Cayley–Hamilton theorem
- *Spread of a matrix
- *Jordan normal form
- *Weyr canonical form
- 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
- *Diagonal matrix, main diagonal
- **Diagonalizable matrix
- *Triangular matrix
- *Tridiagonal matrix
- *Block matrix
- *Sparse matrix
- *Hessenberg matrix
- *Hessian matrix
- *Vandermonde matrix
- *Stochastic matrix
- *Toeplitz matrix
- **Circulant matrix
- *Hankel matrix
- *(0,1)-matrix
Matrix decompositions
Matrix decomposition- Cholesky decomposition
- LU decomposition
- QR decomposition
- Polar decomposition
- Reducing subspace
- Spectral theorem
- Singular value decomposition
- *Higher-order singular value decomposition
- Schur decomposition
- *Schur complement
- *Haynsworth inertia additivity formula
Relations
Computations
- Elementary row operations
- Householder transformation
- Least squares, linear least squares
- Gram–Schmidt process
- Woodbury matrix identity
Vector spaces
Vector space- 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
Multilinear algebra- Tensor
- *Classical treatment of tensors
- *Component-free treatment of tensors
- *Gamas's Theorem
- Outer product
- Tensor algebra
- *Exterior algebra
- *Symmetric algebra
- *Clifford algebra
- *Geometric algebra
Topics related to affine spaces
Affine space- Affine transformation
- Affine group
- Affine geometry
- Affine coordinate system
- Flat (geometry)
- Cartesian coordinate system
- Euclidean group
- Poincaré group
- Galilean group