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# - A bit of math: vectors, tensors, Fourier transform, etc.

DOI link for - A bit of math: vectors, tensors, Fourier transform, etc.

- A bit of math: vectors, tensors, Fourier transform, etc. book

# - A bit of math: vectors, tensors, Fourier transform, etc.

DOI link for - A bit of math: vectors, tensors, Fourier transform, etc.

- A bit of math: vectors, tensors, Fourier transform, etc. book

## 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.