Perron-Frobenius theory

[pe′rōn frō′bā·nē·u̇s ‚thē·ə·rē]

(mathematics)

The study of positive matrices and their eigenvalues; in particular, application of the Perron-Frobenius theorem.

References in periodicals archive ?

Based on the nonlinear Perron-Frobenius theory, we will develop the theory to rigorously formalize the model from a mathematical viewpoint (existence, uniqueness, maximality).

MAGNET: Models and Algorithms for Graph centrality grounded on Nonlinear Eigenvalues Techniques

Samelson developed independently in considering Perron-Frobenius Theory in finite dimensions.

Positive Dynamical Systems in Discrete Time: Theory, Models, and Applications

By the Perron-Frobenius theory, [rho](G) has multiplicity one and exists a unique positive unit eigenvector corresponding to [rho](G).

The smallest spectral radius of graphs with a given clique number

Sections start with coverage of vector spaces, progressing to linear operators and matrices, the duality of vector spaces, determinants, invariant subspaces, inner-product spaces, structure theorems, and additional topics such as functions of an operator, quadratic forms, Perron-Frobenius theory, stochastic matrices, and representations of finite groups.

A (terse) introduction to linear algebra

In addition to theoretical foundation and the latest work in Hilbert geometry, this overview for students and researchers covers relationships between Hilbert geometry and other subjects in mathematics, such as convexity theory, Perron-Frobenius theory, partial differential equations, ergodic theory, and Lie groups.

Handbook of Hilbert Geometry

By the well-known Perron-Frobenius theory, [rho](G) is simple and has a unique positive unit eigenvector and so does q(G).

On the signless Laplacian spectral radius of bicyclic graphs with perfect matchings