# Define Hermitian Matrices.

Matrices
Define Hermitian Matrices.

2020-10-19
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.