Mass in special relativity (including the kinetic energy of the gas) only when it is measured in the center of momentum frame. Just as is the case for single particles, the calculated "rest mass" of such a container of gas does not change when it is in motion, although its "relativistic mass" does change. The container may even be subjected to a force which gives it an overall velocity, or else (equivalently) it may be viewed from an inertial frame in which it has an overall velocity (that is, technically, a frame in which its center of mass has a velocity). In this case,
Cross product The cross product with n therefore describes the infinitesimal generator of the rotations about n. These infinitesimal generators form the Lie algebra so(3) of the rotation group SO(3), and we obtain the result that the Lie algebra R with cross product is isomorphic to the Lie algebra so(3). The vector cross product also can be expressed as the product of a skew-symmetric matrix and a vector: where superscript refers to the transpose operation, and [a] is defined by: The columns [a] of the skew-symmetric matrix for a vector a can be also obtained by calculating the cross product with unit