# Define Hermitian Matrices.

Define Hermitian Matrices.
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Khribechy
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
${a}_{ij}={\overline{a}}_{ji}$
Step 2
For example, consider the matrix
$A=\left[\begin{array}{cc}1& -i\\ i& 1\end{array}\right]$
$\overline{A}=\left[\begin{array}{cc}1& i\\ -i& 1\end{array}\right]$
${\overline{A}}^{T}=\left[\begin{array}{cc}1& -i\\ i& 1\end{array}\right]$
${\overline{A}}^{T}=A$
Therefore, A is hermitian matrix.
Jeffrey Jordon