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Linear Relations and the Kronecker Canonical Form

Thomas BergerCarsten TrunkHenrik Winkler

出版	Techn. Univ., Inst. für Mathematik, 2015
URL	http://books.google.com.hk/books?id=44D3vQEACAAJ&hl=&source=gbs_api

註釋

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 concise: For linear relations the Kronecker canonical form is the analogue of the Jordan canonical form for matrices.