Hermitian Matrix

Q.

Which of the following represents the condition for a matrix A to be hermitian Matrix. Given that the general element of the matrix is aij.

1. $aij=-\overline{aij}$

2. $aij=\overline{aji}$

3. $aij=-\overline{aji}$

4. $\overline{aij}=-aij$

Q.

Which among the following is/are hermitian matrix

1. $\left[\begin{array}{cc}1& i\\ -i& 1\end{array}\right]$

2. $\left[\begin{array}{ccc}i& i& 5\\ i& -i& 0\\ -5& 0& 3i\end{array}\right]$

3. $\left[\begin{array}{cc}i+1& 3i\\ 3i& i+1\end{array}\right]$

4. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Q.

A matrix with diagonal elements as complex numbers with imaginary part not 0 can never be Hermitian matrix

1. True

2. False

Q.

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

1. True

2. False

Q.

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

1. True

2. False

Q.

A Matrix of any order can be a hermitian matrix

1. True

2. False