In many theoretical and practical questions often it is necessary to deal with systems of the linear and nonlinear differential equations. The decision of such systems is represented enough challenge. Search of ways of simplification of these systems and also a finding of more simple methods of decisions is natural. In certain cases this problem manages to be solved by means of special matrixes - linear and nonlinear projectors. These matrixes submit to laws idempotences concerning binary operation of multiplication and also possess the additional properties, allowing applying them at research Euclid spaces. The rank of each such matrix specifies in possibility to divide n - measured Euclid space on a subspace which dimension is equal to a rank that gives the chance to lead systems to the independent subsystems identical to cages of Jordan. It is available - simplification of systems and also - their integration.