TECHNISCHE UNIVERSITÄT BERLIN The Frobenius-Jordan form of nonnegative matrices

PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

The Influence of the Marked Reduced Graph of a Nonnegative Matrix on the Jordan Form and on Related Properties: A Survey

For a nonnegative matrix P, we discuss the relation of its marked reduced graph to that part of the Jordan form that is associated with the Perron-Frobenius root, to the nonnegativity of the eigenVectors and generalized eigenvectors, to the nonnegativity of solutions of linear equations, and to the asymptotic growth of powers of the matrix. Results are often stated in terms of M-matrices, and s...

Technische Universität Berlin Institut für Mathematik Fundamental Diagrams and Multiple Pedestrian Streams

Technische Universität Berlin Institut für Mathematik Some Fundamental Considerations for the Application of Macroscopic Models in the Field of Pedestrian Crowd Simulation

The Sign-Real Spectral Radius for Real Tensors

In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.