A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, for every linear transformation, there exists exactly one corresponding matrix, and every matrix corresponds to a unique linear transformation. The matrix is an extremely important concept in linear algebra.

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a matrix, and every matrix corresponds to a unique linear transformation. The matrix, and its close relative the determinant, are extremely important concepts in linear algebra, and were first formulated by Sylvester and Cayley.

adjacency matrix | adjoint | alternating sign matrix | antisymmetric matrix | block matrix | Bohr matrix | Bourque-Ligh conjecture | Cartan matrix | circulant matrix | condition number | Cramer's rule | determinant | diagonal matrix | Dirac matrices | eigen decomposition theorem | eigenvector | elementary matrix | elementary row and column operations | equivalent matrix | Fourier matrix | Gram matrix | Hilbert matrix | hypermatrix | identity matrix | ill-conditioned matrix | incidence matrix | irreducible matrix | Kac matrix | least common multiple matrix | LU decomposition | matrix addition | matrix inverse | matrix multiplication | matrix trace | McCoy's theorem | minimal matrix | normal matrix | Pauli matrices | permutation matrix | positive definite matrix | random matrix | rational canonical form | reducible matrix | Roth's removal rule | shear matrix | singular matrix | Smith normal form | sparse matrix | special matrix | square matrix | stochastic matrix | submatrix | symmetric matrix | tournament matrix

high school level (California linear algebra standard)