Groups of Transformations

Yu. I. Dimitrienko
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Yu. I. Dimitrienko: Bauman Moscow State Technical University

Chapter Chapter 3 in Tensor Analysis and Nonlinear Tensor Functions, 2002, pp 129-168 from Springer

Abstract: Abstract Let us return to the three-dimensional Euclidean space ℝ3, and consider linear transformations here. A set of such transformations can constitute a special algebraic structure named a group. In general, the theory of groups, the basis of which was developed by the outstanding French mathematician Galois in the XIXth century, is one of most important parts of algebra nowadays. Groups are widely used not only in mathematics, but also in mechanics, physics, quantum chemistry, crystallophysics etc. The present chapter introduces the concept of a group for the case of linear transformation groups in ℝ3.

Keywords: Linear Transformation; Matrix Representation; Orthogonal Transformation; Symmetry Element; Infinite Order (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-017-3221-5_3

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