“Perron number”的意思、由来-开放百科全书

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Perron number

释义

References

In mathematics, a Perron number is an algebraic integer α which is real and exceeds 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 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 coefficients 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.

References

{{cite book

| last = Borwein
| first = Peter
| authorlink = Peter Borwein
| title = Computational Excursions in Analysis and Number Theory
| publisher = Springer Verlag
| year = 2007
| location =
| url =
| doi =
| id =
| isbn = 0-387-95444-9
| page = 24}}{{Algebraic numbers}}{{Numtheory-stub}}

2 : Algebraic numbers|Graph invariants

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