`pytransform3d.rotations`.cross_product_matrix¶

pytransform3d.rotations.cross_product_matrix(v)[source]¶

Generate the cross-product matrix of a vector.

The cross-product matrix $\boldsymbol{V}$ satisfies the equation

$\boldsymbol{V} \boldsymbol{w} = \boldsymbol{v} \times \boldsymbol{w}.$

It is a skew-symmetric (antisymmetric) matrix, i.e., $-\boldsymbol{V} = \boldsymbol{V}^T$ . Its elements are

$\left[\boldsymbol{v}\right] = \left[\begin{array}{c} v_1\\ v_2\\ v_3 \end{array}\right] = \boldsymbol{V} = \left(\begin{array}{ccc} 0 & -v_3 & v_2\\ v_3 & 0 & -v_1\\ -v_2 & v_1 & 0 \end{array}\right).$

Parameters:

varray-like, shape (3,): 3d vector

Returns:

Varray-like, shape (3, 3): Cross-product matrix

pytransform3d.rotations.cross_product_matrix¶

`pytransform3d.rotations`.cross_product_matrix¶