Question

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.

• A. $aij=-\overline{aij}$
• B. $aij=\overline{aji}$
• C. $aij=-\overline{aji}$
• D. $\overline{aij}=-aij$

Answer 1

The correct option is B

$aij=\overline{aji}$

Try to remember the definition of hermitian matrix. A square matrix is hermitian if it ia equal to its conjugate transpose.

We know that if we take an element aij from a square matrix. The corresponding element in its transpose will be aji. If we take both transpose and conjugate the corresponding element becomes $\overline{aji}$. So by definition we can say, $\overline{aji}=aij$.

Or,

$aij=\overline{aji}$. Which is the required condition as per the definition