Perron number

This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "Perron number" – news · newspapers · books · scholar · JSTOR (April 2024)

In mathematics, a Perron number is an algebraic integer α which is real and greater than 1, but such that its conjugate elements are all less than α in absolute value. For example, the larger of the two roots of the irreducible polynomial ${\displaystyle x^{2}-3x+1}$ is a Perron number.

Perron numbers are named after Oskar Perron; the Perron–Frobenius theorem asserts that, for a real square matrix with positive algebraic entries whose largest eigenvalue is greater than one, this eigenvalue is a Perron number. As a closely related case, the Perron number of a graph is defined to be the spectral radius of its adjacency matrix.

Any Pisot number or Salem number is a Perron number, as is the Mahler measure of a monic integer polynomial.

• Borwein, Peter (2007). Computational Excursions in Analysis and Number Theory. Springer Verlag. p. 24. ISBN 0-387-95444-9.

This number theory-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e

This graph theory-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e