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Euclidean space

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Noun1.Euclidean space - a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
metric space - a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality


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The axioms defining a vector space are satisfied simply because at the algebraic level the vector space in question is the familiar Euclidean space of real numbers.
The most influential paper Gerard Salton never wrote by Dubin, David / Library Trends
Jones, Lebesgue Integration on Euclidean Space, Jones and Bartlett Publishers (1993).
Simulation of an Austenite-twinned-Martensite interface by Melara, L.A., Jr. / Journal of Research of the National Institute of Standards and Technology
When viewed in the Euclidean space of a computer screen, this structure appears strangely distorted.
Recipes for artificial realities: intriguing images emerge from a ... by Peterson, Ivars / Science News
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