This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices.
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 Bohemian matrices
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 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 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
Projective space Projective space
Projective transformation Projective geometry Projective linear group Quadric and conic section
See also Glossary of linear algebra Glossary of tensor theory