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Distances on Numbers, Polynomials, and Matrices

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Abstract

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

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References

  1. Barbaresco F. Information Geometry of Covariance Matrix: Cartan–Siegel Homogeneous Bounded Domains, Mostow–Berger Fibration and Frechét Median, in Matrix Information Geometry, Bhatia R. and Nielsen F. (eds.) Springer, Berlin, 2012

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  2. Copson E.T. Metric Spaces, Cambridge University Press, Cambridge, 1968.

    Book  MATH  Google Scholar 

  3. Ernvall S. On the Modular Distance, IEEE Trans. Inf. Theory, Vol. 31-4, pp. 521–522, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  4. Giles J.R. Introduction to the Analysis of Metric Spaces, Australian Math. Soc. Lecture Series, Cambridge University Press, Cambridge, 1987.

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  5. Hamilton W.R. Elements of Quaternions, Chelsea, New York, 1969. Second edition 1899–1901 enlarged by C.J. Joly reprinted.

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© 2013 Springer-Verlag Berlin Heidelberg

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Deza, M.M., Deza, E. (2013). Distances on Numbers, Polynomials, and Matrices. In: Encyclopedia of Distances. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30958-8_12

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