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 dispersion Velocity dispersion In astronomy, the velocity dispersion ("σ") is the statistical dispersion of velocities about the mean velocity for a group of objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or supercluster. By measuring the radial velocities of its members, the velocity dispersion of a cluster can be estimated and used to derive the cluster's mass from the virial theorem. Radial velocity is found by measuring the Doppler width of spectral lines of a collection of objects. The more radial velocities one measures, the more accurately one knows their dispersion. A central velocity dispersion refers to the