pytransform3d.rotations.cross_product_matrix

pytransform3d.rotations.cross_product_matrix(v)

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

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

The function can also be used to compute the logarithm of rotation from a compact axis-angle representation.

Parameters:

varray-like, shape (3,)

3d vector

Returns:

Varray, shape (3, 3)

Cross-product matrix