Cross product "matrix", then it can be generalized in an arbitrary number of dimensions. In mechanics, for example, the angular velocity can be interpreted either as a pseudovector formula_167 or as a anti-symmetric matrix or skew-symmetric tensor formula_168. In the latter case, the velocity law for a rigid body looks: where Ω is formally defined from the rotation matrix formula_170 associated to body's frame: formula_171 In three-dimensions holds: In quantum mechanics the angular momentum formula_173 is often represented as an anti-symmetric matrix or tensor. More precisely, it is the result of cross product involving position formula_174 and linear momentum formula_111: Since both
Velocity coordinate system). The radial and angular velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components. The transverse velocity is the component of velocity along a circle centered at the origin. where The "magnitude of the radial velocity" is the dot product of the velocity vector and the unit vector in the direction of the displacement. where The "magnitude of the transverse velocity" is that of the cross product of the unit vector in the direction of the displacement and the velocity vector. It is also the product of