A matrix is a list of lists.
Often one uses the term in a context where one can add and multiply matrices using matrix calculus.
linear algebra, general linear group, special linear group, matrix mechanics, matrix theory, matrix Hopf algebra, matrix Lie algebra, matrix Lie group, classical Lie group, universal localization, tensor calculus, moment of inertia, eigenvalue, characteristic polynomial (Cayley-Hamilton theorem), spectral curve
Special cases: S-matrix, classical r-matrix, density matrix, hermitian matrix, skew-symmetric matrix, quantum Yang-Baxter matrix, random matrix, skew-symmetric matrix
Operations on/with matrices: transpose matrix, [trace, matrix factorization, Gauss decomposition, Gram-Schmidt process]
Determinants and determinant like notions, and special cases: quasideterminant, Berezinian,Jacobian, Pfaffian, hafnian, Wronskian, resultant, discriminant