Graph invariants | Algebraic numbers

Perron number

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. (Wikipedia).

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My #MegaFavNumbers is 2^82589933-1 // The largest Mersenne prime…..yet

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From playlist MegaFavNumbers

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From playlist MegaFavNumbers

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From playlist MegaFavNumbers

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From playlist MIT 6.189 Multicore Programming Primer, January (IAP) 2007

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Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 2)

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From playlist École d’été 2013 - Théorie des nombres et dynamique

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Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 4)

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From playlist École d’été 2013 - Théorie des nombres et dynamique

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From playlist École d’été 2013 - Théorie des nombres et dynamique

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Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 3)

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From playlist MegaFavNumbers

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2¹⁰²⁴ #MegaFavNumbers

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From playlist MegaFavNumbers

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From playlist Mathematics

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From playlist MegaFavNumbers

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Why Argentina is not rich

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From playlist Economics

Related pages

Spectral radius | Adjacency matrix | Graph (discrete mathematics) | Absolute value | Monic polynomial | Mathematics | Mahler measure | Perron–Frobenius theorem | Square matrix | Algebraic integer | Oskar Perron | Salem number