Question

Define Hermitian Matrices.

Matrices
ANSWERED
asked 2020-10-18
Define Hermitian Matrices.

Answers (1)

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.
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