# Cross Product by Matrix Multiplication

For two vectors $\vec{a}$ and $\vec{b}$, the cross product $\vec{a} \times \vec{b}$ can be computed using matrix multiplcation[1] as:

$$\vec{a} \times \vec{b} = A_\times \vec{b}$$

where $A_\times$ is defined as:

$$A_\times = \begin{bmatrix} 0 & -a_3 & a_2\\ a_3 & 0 & -a_1\\ -a_2 & a_1 & 0 \end{bmatrix}$$

where $a_1$, $a_2$ and $a_3$ are the components of $\vec{a}$.

[1] https://en.wikipedia.org/wiki/Cross_product#Conversion_to_matrix_multiplication “Cross Product: Conversion to Matrix Multiplication”