Skew symmetric matrix is a square matrix Q=[xij] in which (i, j)th element is negative of the (j, i)th element i.e. xij = -xji for all values of i and j. In other words, a square matrix (Q) which is equal to negative of its transpose is known as skew-symmetric matrix i.e. QT = -Q.
Skew symmetric matrix examples
The example of a skew-symmetric matrix of order 2 (or matrix size is 2 x 2) is given as
\[C=\begin{bmatrix} 0 &2 \\ -2& 0 \end{bmatrix}\]
The example of a skew-symmetric matrix of order 3 (or matrix size is 3 x 3) is given as
\[D=\begin{bmatrix} 0 &8 &2 \\ -8& 0 &5 \\ -2& -5 & 0 \end{bmatrix}\]
Skew symmetric matrix properties
1. All the diagonal elements in a skew-symmetric matrix are always zero.
2. If P be a skew-symmetric matrix then PT = -P.
Let B be any matrix then
1. $\frac{B-B^T}{2}$is always a skew-symmetric matrix.
