Determination of Jordan chains by extended matrices

Abstract

The major obstacle to determination of the Jordan chains for a highly degenerated eigenproblem is that the triangular combinations of the principal vectors in a Jordan chain are also principal vectors and the linear combinations of the eigenvectors of all Jordan blocks associated with the same eigenvalue are also eigenvectors. These indeterminate constants will hide the Jordan block structure and make the analysis very difficult. We propose an extended matrix method to find the Jordan chains and eliminate the indeterminate constants so that the Jordan block structure can be computed sequentially. An example with the Segre characteristic [(321)11] is given.