A (2n+1) DIMENSIONAL LINEAR VECTOR FIELD

It has been shown that the integral curves of a linear vector field X in R3 described by a matrix of the from Can be:1) helices with common axes and the same parametr, if rank [AC]=3. 2)cricles which lie in planes parallel to aech other and which have centers on the axis perpendicular to those paraller planes, if rank [AC]= 2. 3)parallel straight lines, if rank [AC]=1 The results of Karger and Novak are by us to R2n+1. It is shown that all the results are also valid in the general case.

A (2n+1) DIMENSIONAL LINEAR VECTOR FIELD Keywords:

Linear vector field , Helix , Orthonormal basis , Integral curve