HOMOGENEOUS LINEAR DIFFERENTIAL SYSTEMS WITH CONSTANT COEFFICIENTS AND THE PROBLEM OF EIGENVALUES (PART 2)
It is well known that to solve a homogeneous linear differential system with a constant matrix A one must usually find the Jordan canonical form of the matrix A and to obtain a matrix P such that J = P-1AP. To find a matrix J one should rely on the theory of elementary devisors of the characteristic matrix А - Е, which triggers off the so called full problem of eigenvalues. This problem is fraught with difficulty. In 1969 R. Bellman argued that there were no simple ways of calculating eigenvalues and eigenvectors of large matrices. Almost nothing has changed since then. The article suggests a new approach to solution of the problem by first computing eigenvectors and further finding eigenvalues, which is the opposite of the traditionally applied procedure. Part 1 was mainly theoretical and part 2 provides practical illustrations.