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Linear Algebra

List of linear algebra topics; Theorems and definitions in linear algebra
Linear equations: System of linear equations; Determinant; Minor (linear algebra); Cauchy–Binet formula; Cramer's rule; Gaussian elimination; Strassen algorithm
Matrices: Linear algebra; Zero object (algebra); Absolutely convex set; Adjugate matrix; Affine space; Amitsur–Levitzki theorem; Antilinear map; Antiunitary operator; Asymmetric norm; Backus–Gilbert method; Balanced set; Barycentric coordinate system; Basis (linear algebra); Basis function; Bidiagonal matrix; Big M method; Binomial inverse theorem; Bra–ket notation; Bunch–Nielsen–Sorensen formula; Canonical basis; Cartesian tensor; Category of vector spaces; Cauchy–Schwarz inequality; Centrosymmetric matrix; Change of basis; Characteristic polynomial; Choi's theorem on completely positive maps; Coates graph; Codimension; Coefficient matrix; Column space; Column vector; Commutation matrix; Complex conjugate vector space; Complex vector space; Compressed sensing; Computing the permanent; Cone (linear algebra); Conformable matrix; Conjugate transpose; Controlled invariant subspace; Convex cone; Coordinate space; Coordinate vector; CSS code; Defective matrix; Definite quadratic form; Delta operator; Dependence relation; Dieudonné determinant; Dimension (vector space); Direct sum of modules; Direction vector; Dot product; Dual basis; Dual basis in a field extension; Dual norm; Dual number; Dual space; Eigendecomposition of a matrix; Eigengap; Eigenplane; Eigenvalue perturbation; Eigenvalues and eigenvectors; Elementary matrix; Entanglement-assisted stabilizer formalism; Euclidean space; Euclidean vector; Finite dimensional von Neumann algebra; Flag (linear algebra); Flat (geometry); Frame (linear algebra); Frame of a vector space; Fredholm alternative; Fredholm's theorem; Frobenius normal form; Fusion frame; General linear group; Generalizations of Pauli matrices; Generalized eigenvector; Generalized singular value decomposition; Gershgorin circle theorem; Golden–Thompson inequality; Gram–Schmidt process; Hamming space; Haynsworth inertia additivity formula; Hermite normal form; Hilbert space; Hilbert–Poincaré series; Homogeneous coordinates; Homogeneous function; Homogeneous linear equation; Hurwitz determinant; Hyperplane; Identity matrix; Immanant of a matrix; Independent equation; Indeterminate system; Integer points in convex polyhedra; Invariant subspace; Invariants of tensors; Invertible matrix; Joint spectral radius; Jordan normal form; Jordan–Chevalley decomposition; K-frame; K-SVD; Kernel (algebra); Kernel (linear algebra); Lapped transform; Lattice reduction; Leibniz formula for determinants; Levi-Civita symbol; Line segment; Line-line intersection; Linear combination; Linear complementarity problem; Linear equation over a ring; Linear form; Linear independence; Linear inequality; Linear map; Linear span; Linear subspace; List of vector spaces in mathematics; Locally finite operator; Majorization; Matrix addition; Matrix analysis; Matrix calculus; Matrix Chernoff bound; Matrix congruence; Matrix decomposition into clans; Matrix determinant lemma; Matrix difference equation; Matrix norm; Matrix pencil; Mixed linear complementarity problem; Mode of a linear field; Newton's identities; Non-negative matrix factorization; Nonlinear eigenproblem; Nonnegative rank (linear algebra); Norm (mathematics); Normal basis; Null vector; Numerical range; Orientation (vector space); Orthant; Orthogonal basis; Orthogonal complement; Orthogonal diagonalization; Orthogonal Procrustes problem; Orthogonal transformation; Orthogonality; Orthogonalization; Orthographic projection (geometry); Orthonormal basis; Orthonormal function system; Orthonormality; Overcompleteness; Overdetermined system; Pairing; Partial trace; Peetre's inequality; Permanent; Polarization identity; Polynomial basis; Principal angles; 3D projection; Projection (linear algebra); Projection-valued measure; Projectivization; Pseudoscalar; Pseudovector; Purification of quantum state; Quadratic eigenvalue problem; Quadratic form; Quadruple product; Quasinorm; Quaternionic matrix; Quaternionic vector space; Quotient space (linear algebra); Rank (linear algebra); Rank factorization; Rayleigh quotient; 2 × 2 real matrices; Reality structure; Reduction (mathematics); Relative dimension; Resolvent set; Restricted isometry property; Rota's basis conjecture; Rotation operator (vector space); Row and column spaces; Row equivalence; Row space; Row vector; Rule of Sarrus; Scalar (mathematics); Scalar multiplication; Schmidt decomposition; Schur complement; Schur product theorem; Segre classification; Self-adjoint; Semi-simple operator; Semilinear transformation; Sesquilinear form; Seven-dimensional cross product; Shear mapping; Shear matrix; Sherman–Morrison formula; Singular value decomposition; Skew-Hamiltonian matrix; Skew-Hermitian; Special linear group; Spectral theorem; Spectral theory; Spherical basis; Spinors in three dimensions; Split-complex number; Spread of a matrix; Squeeze mapping; Stabilizer code; Standard basis; Standard flag; Steinitz exchange lemma; Stokes operator; Sublinear function; Sylvester's determinant theorem; Sylvester's law of inertia; Symplectic vector space; Tapering (mathematics); Tensor operator; Tikhonov regularization; Toeplitz matrix; Trace (linear algebra); Trace diagram; Trace identity; Transpose; Triangle inequality; Trilinear coordinates; Underdetermined system; Unit vector; Unitary transformation; Vector projection; Vector space; Vector spaces without fields; Vector-valued function; Vectorization (mathematics); Weyl's inequality; Woodbury matrix identity; Z-order curve; Zech's logarithms; Zero mode; Matrix (mathematics); Matrix multiplication