Inhalt des Dokuments
Preprint
The Frobenius-Jordan form of nonnegative matrices
Author(s) :
Volker Mehrmann
,
Manideepa Saha
Preprint series of the Institute of Mathematics, Technische Universität Berlin
MSC 2000
- 15A48 Positive matrices and their generalizations; cones of matrices
-
15A21 Canonical forms, reductions, classification
Abstract :
In this paper we use preferred and quasi-preferred bases of generalized eigenspaces associated with the spectral radius of nonnegative matrices to analyze the existence and uniqueness of a variant of the Jordan canonical form which we call Frobenius-Jordan form. It is a combination of the classical Jordan canonical form in the part associated with the eigenvalues that are different from the spectral radius, while it is like the Frobenius normal form in the part associated with the spectral radius.
Based on the Frobenius-Jordan form, spectral and combinatorial properties of nonnegative matrices are discussed. In particular, we analyze the existence of nonnegative graph representations
of the generalized eigenspace associated with the spectral radius.
Keywords :
Preferred basis, quasi-preferred basis, Frobenius-Jordan form