What is Skew Hermitian Matrix? Example

When the conjugate transpose of a complex square matrix is equal to the negative of itself, then this matrix is called as skew hermitian matrix. If P is a complex square matrix and if it satisfies Pθ = -P then such matrix is termed as skew hermitian. It is noted that Pθ represents the conjugate transpose of matrix P.

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


Skew Hermitian matrix examples

The example of a skew hermitian matrix of size is 2 x 2 is given as

    \[A=\begin{bmatrix} 0 &-2-3i \\ 2-3i& 0 \end{bmatrix}\]

The example of skew hermitian matrix of size is 3 x 3 is given as

    \[B=\begin{bmatrix} 0 &i &2-i \\ -i& 0 &1-i \\ -2+i&-1+i & 0 \end{bmatrix}\]

Note: For skew hermitian matrix, the diagonals elements are always equal to zero.

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