Euclidean, Pseudo-Euclidean, Conformal and Pseudoconformal Geometries
In 0.5.3 we have defined the real Euclidean space R n as the affine space E n whose vectors satisfy axioms E.1° – 5°. Since the inner product x 2 of a vector x = x 2 e i of this space by itself is a positive definite quadratic form x 2 = e ij x i x j , this space is also called a quadratic Euclidean space. In 0.5.3 we have seen that the space R n also satisfies the axioms M.1° – 3° of a metric space.
KeywordsGreat Circle Conformal Transformation Fractional Linear Transformation Steiner Triple System Real Plane
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