Spacetime as a redshift and analyze the effect in terms of scenarios (b) or (d). In classical mechanics, the state of motion of a particle is characterized by its mass and its velocity. Linear momentum, the product of a particle's mass and velocity, is a vector quantity, possessing the same direction as the velocity: p = "mv". It is a "conserved" quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In relativistic mechanics, the momentum vector is extended to four dimensions. Added to the momentum vector is a time component that
Tensor product of modules in its right argument: In the general case, each element of the tensor product of modules gives rise to a left "R"-linear map, to a right "R"-linear map, and to an "R"-bilinear form. Unlike the commutative case, in the general case the tensor product is not an "R"-module, and thus does not support scalar multiplication. Both cases hold for general modules, and become isomorphisms if the modules "E" and "F" are restricted to being finitely generated projective modules (in particular free modules of finite ranks). Thus, an element of a tensor product of modules over a ring "R" maps canonically