A symmetric matrix is a square matrix that satisfies A^T = A, where A^T denotes the transpose, so a_(i j) = a_(j i). This also implies A^(-1) A^T = I, where I is the identity matrix. For example, A = [4 | 1 1 | -2] is a symmetric matrix. Hermitian matrices are a useful generalization of symmetric matrices for complex matrices. A matrix that is not symmetric is said to be an asymmetric matrix, not to be confused with an antisymmetric matrix.

antihermitian matrix | antisymmetric matrix | asymmetric matrix | bisymmetric matrix | conjugate transpose | Hankel matrix | Hermitian matrix | orthogonal matrix | symmetric part