Every complex matrix can be broken into a Hermitian part A_H congruent 1/2(A + A^H) (i.e., A_H is a Hermitian matrix) and an antihermitian part A_AH congruent 1/2(A - A^H) (i.e., A_AH is an antihermitian matrix). Here, A^H denotes the adjoint.

antihermitian matrix | antihermitian part | antisymmetric matrix | antisymmetric part | conjugate transpose | Hermitian matrix | symmetric matrix | symmetric part