Symmetric and antisymmetric matrices
A square matrix is symmetric when and antisymmetric when .
Definition 3.16 (Symmetric and Antisymmetric Matrices)
If is a square matrix, then is
- symmetric if ,
- antisymmetric if
Decomposition into parts
Every square matrix with real entries decomposes as , where
are the symmetric and antisymmetric parts. Since and , the symmetric part further splits into the traceless symmetric matrix , with , together with the isotropic part :
Related
Stated in
- Definition 3.16 (Symmetric and Antisymmetric Matrices)§3.4.4 Transpose and Hermitian Conjugate