A system of linear equations

Determinant, minor, cofactor, and inverse matrices

Gaussian elimination and Gauss-Jordan elimination

LU decomposition

Vector space, vector norm, and distance

Normal matrices, Hermitian matrices, positive semidefinite matrices, unitary matrices, and orthogonal matrices

Spectral decomposition, eigenvalues, and eigenvectors

Matrix norms and spectral norm

Condition number

Conjugate gradient method

Gauss–Seidel method and Jacobi method

Gershgorin Circle Theorem

Power method and inverse power method

Householder tridiagonalization

QR decomposition and QR algorithm

Singular value decomposition (SVD): singular values, left singular vectors, and right singular vectors