Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598812 | Linear Algebra and its Applications | 2016 | 32 Pages |
Abstract
We show that the Kronecker canonical form (which is a canonical decomposition for pairs of matrices) is the representation of a linear relation in a finite dimensional space. This provides a new geometric view upon the Kronecker canonical form. Each of the four entries of the Kronecker canonical form has a natural meaning for the linear relation which it represents. These four entries represent the Jordan chains at finite eigenvalues, the Jordan chains at infinity, the so-called singular chains and the multi-shift part. Or, to state it more concisely: For linear relations the Kronecker canonical form is the analogue of the Jordan canonical form for matrices.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Thomas Berger, Carsten Trunk, Henrik Winkler,