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In this chapter, we encounter more advanced topics related to geometry, possible through use of one or more bilinear forms. Along the way we discuss, once again, models of reality and introduce the relativity principle, the Mazur-Ulam theorem, the Cartan-Dieudonné theorem, the Euclidean and Galilean groups, the Lorentz and Poincare groups, and conclude with an analysis of symplectic matrices.

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Geometry Associated With Real Bilinear Forms

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  • 发表日期：

    2025年

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  • Lawrence Susanka

摘要

In this chapter, we encounter more advanced topics related to geometry, possible through use of one or more bilinear forms. Along the way we discuss, once again, models of reality and introduce the relativity principle, the Mazur-Ulam theorem, the Cartan-Dieudonné theorem, the Euclidean and Galilean groups, the Lorentz and Poincare groups, and conclude with an analysis of symplectic matrices.