Distances on Numbers, Polynomials, and Matrices

Michel Marie Deza and Elena Deza
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Michel Marie Deza: Ecole Normale Supérieure
Elena Deza: Moscow State Pedagogical University

Chapter Chapter 12 in Encyclopedia of Distances, 2016, pp 229-246 from Springer

Abstract: Abstract Here we consider the most important metrics on the classical number systems: the semiring $$\mathbb{N}$$ of natural numbers, the ring $$\mathbb{Z}$$ of integers, and the fields $$\mathbb{Q}$$ , $$\mathbb{R}$$ , $$\mathbb{C}$$ of rational, real, complex numbers, respectively. We consider also the algebra $$\mathcal{Q}$$ of quaternions.

Keywords: Matrix Norm; Complex Modulus; Frobenius Norm; Irreducible Polynomial; Natural Norm (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-52844-0_12

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DOI: 10.1007/978-3-662-52844-0_12

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