Perron number
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 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.
References
- Borwein, Peter (2007). Computational Excursions in Analysis and Number Theory. Springer Verlag. p. 24. ISBN 0-387-95444-9.
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- Algebraic integer
- Chebyshev nodes
- Constructible number
- Conway's constant
- Cyclotomic field
- Doubling the cube
- Eisenstein integer
- Gaussian integer
- Golden ratio (φ)
- Perron number
- Pisot–Vijayaraghavan number
- Plastic ratio (ρ)
- Quadratic irrational number
- Rational number
- Root of unity
- Salem number
- Silver ratio (δS)
- Square root of 2
- Square root of 3
- Square root of 5
- Square root of 6
- Square root of 7
- Supergolden ratio (ψ)
- Supersilver ratio (ς)
- Twelfth root of 2
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