Engineering Journal: Science and InnovationELECTRONIC SCIENCE AND ENGINEERING PUBLICATION
Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
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Article

Weil — Rashevskiy axiomatic system in analitic geometry and higher algebra

Published: 10.10.2013

Authors: Kuznetsov V.V., Mastihin A.V.

Published in issue: #5(17)/2013

DOI: 10.18698/2308-6033-2013-5-742

Category: Engineering education

We consider Weil-Roshevskiy axiomatic system os adopted variant of the point-vector axiomatic system for affine space, which is the basement of the analytic geometry and algebra of finite-dimensional spaces. It gives us an opportunity to obtain strictly proved statements in vector algebra. We give here four groups of axioms and а set of traditionally proved theorems, some of them with proof. A construction of affine manifold (n-dimensional plane) possesses а geometric meaning of the generalization of the line and the plane. In this connection we consider on exercise of reducing a parametric vector equation of n-dimensional plane to matrix equation. Also we discuss the notions of geometrically dependent vector set, convex span, and simplex.