Question

The following matrix is HERMATIAN Matrix $\left[\begin{array}{ccc}1& -i& 5\\ i& 5& 0\\ 5& 0& 3\end{array}\right]$

• A. True
• B. False

Answer 1

The correct option is A

True

We already saw that a Hermitian matrix is a square matrix with complex entries that is equal to its own conjugate Transpose.

Here in option a : the transpose will be $\left[\begin{array}{ccc}1& i& 5\\ -i& 5& 0\\ 5& 0& 3\end{array}\right]$

the conjugate of this will be $\left[\begin{array}{ccc}1& -i& 5\\ i& 5& 0\\ 5& 0& 3\end{array}\right]$ which is same as original matrix

Therefore it is a Hermitian matrix.