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 
.
Skew Hermitian matrix examples
The example of a skew hermitian matrix of size is 2 x 2 is given as
![\[A=\begin{bmatrix} 0 &-2-3i \\ 2-3i& 0 \end{bmatrix}\]](https://electricalvoice.com/wp-content/ql-cache/quicklatex.com-919de86cddbbf9d148fd93dbe756e967_l3.png "Rendered by QuickLaTeX.com")
The example of skew hermitian matrix of size is 3 x 3 is given as
![\[B=\begin{bmatrix} 0 &i &2-i \\ -i& 0 &1-i \\ -2+i&-1+i & 0 \end{bmatrix}\]](https://electricalvoice.com/wp-content/ql-cache/quicklatex.com-77efb1b194afecac1700da0a202eb550_l3.png "Rendered by QuickLaTeX.com")
Note: For skew hermitian matrix, the diagonals elements are always equal to zero.
