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arXiv · 0710.1313

Semi--vector spaces and units of measurement

Josef Janyška·Marco Modugno·Raffaele Vitolo
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Abstract

This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of ``positive space'' and its rational powers. Positive spaces are 1-dimensional ``semi-vector spaces'' without the zero vector. A direct approach to this subject might be sufficient. On the other hand, a broader mathematical understanding requires the notions of sesqui- and semi-tensor products between semi-vector spaces and vector spaces. So, the paper is devoted to an original contribution to the algebraic theory of semi-vector spaces, to the algebraic analysis of positive spaces and, eventually, to the algebraic model of physical scales and units of measurement in terms of positive spaces.

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Josef Janyška, Marco Modugno, Raffaele Vitolo. 2007-10-05. Semi--vector spaces and units of measurement. https://arxiv.org/abs/0710.1313

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