express matrix A as a skew symmetric and symmetric matrix

Question

express matrix A as a skew symmetric and symmetric matrix

Answer 1

If we denote A^T as the transpose of the original matrix, then by definition

1. The symmetric part of A is given as S=(A+A^T)/2
2. The skew-symmetric (antisymmetric) part of A is K=(A-A^T)/2

 

S should have the property that S=S^T, and K should satisfy -K=K^T. Additionally, A=S+K, which you can verify by directly summing the formulas for S and K.