Step 1

Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose, that is for which

\(A=A^H\)

where \(A^H\) denotes the conjugate transpose.

In other words, we can say the matrix whose matrix whose element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column is called Hermitian matrix.

That is

\(a_{ij}=\bar{a}_{ji}\)

Step 2

For example, consider the matrix

\(A=\begin{bmatrix}1 & -i \\i & 1 \end{bmatrix}\)

\(\bar{A}=\begin{bmatrix}1 & i \\ -i & 1 \end{bmatrix}\)

\(\bar{A}^T=\begin{bmatrix}1 & -i \\i & 1 \end{bmatrix}\)

\(\bar{A}^T=A\)

Therefore, A is hermitian matrix.

Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose, that is for which

\(A=A^H\)

where \(A^H\) denotes the conjugate transpose.

In other words, we can say the matrix whose matrix whose element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column is called Hermitian matrix.

That is

\(a_{ij}=\bar{a}_{ji}\)

Step 2

For example, consider the matrix

\(A=\begin{bmatrix}1 & -i \\i & 1 \end{bmatrix}\)

\(\bar{A}=\begin{bmatrix}1 & i \\ -i & 1 \end{bmatrix}\)

\(\bar{A}^T=\begin{bmatrix}1 & -i \\i & 1 \end{bmatrix}\)

\(\bar{A}^T=A\)

Therefore, A is hermitian matrix.