  Classical and quantum mechanics for an extended Heisenberg algebra with
canonical commutation relations for position and momentum coordinates are
considered. In this approach additional noncommutativity is removed from the
algebra by linear transformation of phase space coordinates and transmitted to
the Hamiltonian (Lagrangian). This transformation does not change the quadratic
form of Hamiltonian (Lagrangian) and Feynman's path integral maintains its
well-known exact expression for quadratic systems. The compact matrix formalism
is presented and can be easily employed in particular cases. Some p-adic and
adelic aspects of noncommutativity are also considered.
