An efficient Jordan basis algorithm

Most algorithms for determining a Jordan basis for an endomorphism of a finite dimensional vector space suffer from the major drawback that they are computationally inefficient. In this paper, a universal and efficient algorithm for an endomorphism of a finite dimensional vector space over an arbitrary field is presented. Three computational examples are considered which show how our new algorithm works. A computational comparison to the Jordan basis algorithm in Kudo et al. (2010) completes the paper (algorithmic aspects).