cross product (idea)

The cross product for two 3D vectors can be expressed as a matrix operator. That is, for every 3-vector v, there is a 3×3 matrix V such that, for every 3-vector w,

V w = v × w.

Given that v = (v_x, v_y, v_z)^T, this matrix V is denoted cross(v) and is defined by the skew-symmetric matrix

           |  0  -vz  vy |
cross(v) = |  vz  0  -vx |
           | -vy  vx  0  |.

This matrix is useful in defining the arbitrary 3D rotation matrix and in finding the angular velocity vector.