Any square matrix A can be written as a sum A = A_S + A_A, where A_S = 1/2(A + A^T) is a symmetric matrix known as the symmetric part of A and A_A = 1/2(A - A^T) is an antisymmetric matrix known as the antisymmetric part of A. Here, A^T is the transpose.

antisymmetric matrix | antisymmetric part | symmetric matrix | symmetric tensor