Linear equations System of linear equations Determinant Minor (linear algebra) Cramer's rule Gauss-Jordan elimination Matrices List of matrices, glossary of matrix theory Stochastic matrix Toeplitz matrix Matrix theory Matrix multiplication Characteristic polynomial Trace (matrix) Cayley-Hamilton theorem Eigenvalue, eigenvector Jordan normal form Rank (matrix theory) Matrix inversion Adjugate Transpose Dot product Symmetric matrix Orthogonal matrix Skew-symmetric matrix Conjugate transpose Unitary matrix Hermitian matrix Positive definite, positive semidefinite Diagonal matrix, main diagonal Spectral theorem Decompositions Cholesky decomposition LU decomposition Singular value decomposition Schur complement Vectorss Scalar multiplication Linear combination Linear span Linear independence Basis (linear algebra) Vector spaces Dimension theorem for vector spaces Linear transformation Galilean transformation, Lorentz transformation Column space Row space Null space, nullity Rank-nullity theorem Dual space Linear function Linear functional Orthogonality Category of vector spaces Multilinear algebra Tensor Classical treatment of tensors Intermediate treatment of tensors Component-free treatment of tensors Affine space Affine transformation Affine group Affine geometry