Skew-Symmetric Matrix

Skew-Symmetric

Skew-symmetric matrix means that $\mathbf{A}$ satisfies ${\mathbf{A}}^T=-\mathbf{A}$.

The $\wedge$ operator is a skew-symmetric symbol, which means writing $\mathbf{a}$ as a skew-symmetric matrix, where:

$${\mathbf{a}}^{\wedge }=\left[\begin{array}{ccc}0& -a_3& a_2\\ a_3& 0& -a_1\\ -a_2& a_1& 0\end{array}\right]$$

The turns the outer product $a\times b$ into the multiplication of the matrix $a^{\wedge }$ and the matrix $b$, which is a linear operation.