Question 256769
A Hermitian matrix (or self-adjoint matrix) is a square matrix with complex entries which is equal to its own conjugate transpose – that is, the element in the ith row and jth column is equal to the complex conjugate of the element in the jth row and ith column, for all indices i and j:

    a_{i,j} = \overline{a_{j,i}}.

If the conjugate transpose of a matrix A\; is denoted by A^\dagger, then the Hermitian property can be written concisely as

    A = A^\dagger.

Hermitian matrices can be understood as the complex extension of a real symmetric matrix.