ABSTRACT
A tensor of rank two Tik is a hermitian tensor, if Tki = T ∗ ik, and it is an
antihermitian one, if Tki = −T ∗ik. Any tensor Tik can be represented as a superposition of the hermitian tensor T
(H) ik and the antihermitian one T
Tik = T (H) ik + T
(A) ik , T
2 (Tik + T
∗ ki), T
2 (Tik − T ∗ki)
Vector ~A is called an eigenvector of a matrix Tik, if TikAk = λAi, where λ is the respective eigenvalue of this matrix ( summation over “dumb” indices, in this case over the index k, is assumed). If matrix Tik is a hermitian one, then all its eigenvalues are real and, vice versa, all eigenvalues of an antihermitian matrix are imaginary.
