  The relation between nonlinear algebras and linear ones is established. For
one-dimensional nonlinear deformed Heisenberg algebra with two operators we
find the function of deformation for which this nonlinear algebra can be
transformed to a linear one with three operators. We also establish the
relation between Lie algebra of total angular momentum and corresponding
nonlinear one. This relation gives a possibility to simplify and to solve the
eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction
of this problem to the case of linear algebra. It is demonstrated on the
example of harmonic oscillator.
