What is Hermitian Matrix? Example

When the conjugate transpose of a complex square matrix is equal to itself, then such matrix is known as hermitian matrix. If B is a complex square matrix and if it satisfies Bθ = B then such matrix is termed as hermitian. Here Bθ represents the conjugate transpose of matrix B.

The conjugate transpose of a matrix ‘B’ is also denoted by B^* or (\overline{B})^T


Hermitian matrix examples

The example of a hermitian matrix of size is 2 x 2 is as follows.

    \[A=\begin{bmatrix} 1 &2+3i \\ 2-3i& 6 \end{bmatrix}\]

The example of hermitian matrix of size is 3 x 3 is as follows.

    \[D=\begin{bmatrix} 1 &i &2+i \\ -i& 2 &1-i \\ 2-i&1+i & 2 \end{bmatrix}\]

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