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Outline of linear algebra

Last updated October 23, 2025

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
Matrices
Matrix decompositions
Relations
Computations
Vector spaces
Structures
Multilinear algebra
Topics related to affine spaces
Projective space
See also

Linear equations

Linear equation

Matrices

Matrix

Matrix decompositions

Matrix decomposition

Relations

Computations

Structures

Multilinear algebra

Topics related to affine spaces

Affine space

Projective space

v t e Linear algebra
Outline Glossary Template:Matrix classes
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 Spectrum Trace Eigenvalue, eigenvector and eigenspace Cayley–Hamilton theorem Jordan normal form Weyr canonical form Rank Inverse, Pseudoinverse Adjugate, Transpose Dot product Symmetric matrix, Skew-symmetric matrix Orthogonal matrix, Unitary matrix Hermitian matrix, Antihermitian matrix Positive-(semi)definite Pfaffian Projection Spectral theorem Perron–Frobenius theorem Diagonal 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 List of matrices
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 Reducing subspace
Relations and computations	Matrix equivalence Matrix congruence Matrix similarity Matrix consimilarity Row equivalence 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 Basis, Hamel basis Change of basis Dimension theorem for vector spaces Hamel dimension Examples of vector spaces Linear map Shear mapping Squeeze mapping Linear subspace Row and column spaces, Null space Rank–nullity theorem Nullity theorem Cyclic subspace Dual space, 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 Improper rotation Symplectic structure
Multilinear algebra	Multilinear algebra Tensor Tensors (classical) Component-free treatment of tensors Outer product Tensor algebra Exterior algebra Symmetric algebra Clifford algebra Geometric algebra Bivector Multivector Gamas's theorem
Affine and projective	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 transformation Projective geometry Projective linear group Quadric
Numerical linear algebra	Numerical linear algebra Floating-point arithmetic Numerical stability Basic Linear Algebra Subprograms Sparse matrix Comparison of linear algebra libraries
Category

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