| 释义 |
- Linear equations
- Matrices
- Matrix decompositions
- Relations
- Computations
- Vector spaces
- Structures
- Multilinear algebra
- Affine space and related topics
- Projective space
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
- Cayley–Hamilton theorem
- Spread of a matrix
- Jordan normal form
- Weyr canonical form
- Rank
- Matrix inversion, invertible matrix
- 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- Cholesky decomposition
- LU decomposition
- QR decomposition
- Polar decomposition
- Spectral theorem
- Singular value decomposition
- Higher-order singular value decomposition
- Schur decomposition
- Schur complement
- Haynsworth inertia additivity formula
Relations- Matrix equivalence
- Matrix congruence
- Matrix similarity
- Matrix consimilarity
- Row equivalence
Computations- Elementary row operations
- Householder transformation
- Least squares, linear least squares
- Gram–Schmidt process
- Woodbury matrix identity
Vector spaces- Linear combination
- Linear span
- Linear independence
- Scalar multiplication
- Basis
- Change of basis
- Hamel basis
- Cyclic decomposition theorem
- Dimension theorem for vector spaces
- 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)
- Symplectic structure
Multilinear algebra- Tensor
- Classical treatment of tensors
- Component-free treatment of tensors
- Outer product
- Tensor algebra
- Exterior algebra
- Symmetric algebra
- Clifford algebra
- Geometric algebra
Affine space and related topics- Affine transformation
- Affine group
- Affine geometry
- Affine coordinate system
- Flat (geometry)
- Cartesian coordinate system
- Euclidean group
- Poincaré group
- Galilean group
Projective space- Projective transformation
- Projective geometry
- Projective linear group
- Quadric and conic section
{{Linear algebra}} 4 : Mathematics-related lists|Linear algebra|Wikipedia outlines|Lists of topics |