Diagonal entries of an Hermitian matrix are real A matrix $A$ is Hermitian if $A=A^*$ where $A^* = (\bar A)^T$. I read in a book that the diagonal entries of every hermitian matrix is real. I really can not understand why it is true.

Thanks
Take a simple example of a 1-dimensional complex matrix: $[a+ib]$.
To be hermitian, you need to show that $[a+ib]=\overline{[a+ib]}=[a-ib]$, hence $b=0$.
When you take the transpose, the diagonal entries will not change the position. Then after taking the conjugate, the diagonal entries should be the same. That means they must be real.