A direct proof of theorem on generalized Jordan form of linear operators

Abstract

The present paper gives a direct proof of the following result: for any linear operator over arbitrary field there exists a basis in which it has a polyquasicyclic matrix, i.e. a generalized Jordan form of second kind. The polyquasicyclic form of a linear operator is uniquely determined up to the order of direct summands on the diagonal, and it is shown that the generalized Jordan form of second kind is a link that connects the classical Jordan form and the rational canonical form.