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Classification of the Equations of the Second Order Surfaces in Space R⁴ . Non-Degenerated case
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UDC: 51(071)
Publication Language: Russian
Stuc. intelekt. 2012; 17(4):361-369
Abstract: In the paper, the matrix method for classification of the second order surfaces in space R⁴ is developed. This method is based on the analysis of the 5-th order symmetrical quadratic matrix. The matrix is built with three coefficients of the quadratic form of four variables. Such matrix produces 25 monomial 5-th order matrices. These matrices give 14 simplest equations of elliptic, hyperbolic and parabolic types of surfaces.
Keywords: canonical, surface, ellipsoid, hyperboloid, paraboloid, space 4 R , matrix, monomial matrix, canonical equation
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