With Cartesian coordinates it is modelled by the real coordinate space ( ) of the same dimension.
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It begins by defining something called " real coordinate space " : that's a vector space.
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Thus, a real coordinate space together with this Euclidean structure is called "'Euclidean space " '.
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Bearing this in mind, a manifold looks locally like [ [ real coordinate space | ] ] at every point.
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Then it has a section saying that Euclidean space is " more than just real coordinate space " : that's the diff.
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The LogSumExp function domain is \ R ^ n, the real coordinate space, and its range is \ R, the real line.
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The real and imaginary parts of the coordinates set up a bijection of \ mathbb C ^ n with the real coordinate space \ mathbb R ^ { 2n }.
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Since the right-hand side of the identity is clearly non-negative, it implies finite-dimensional real coordinate space ! " n " and its complex counterpart ! " n ".
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In modern presentations of Euclidean geometry, the points of space are defined in terms of their Cartesian coordinates, and Euclidean space itself is commonly identified with the real coordinate space "'R " "'n ".
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In mathematics, "'real coordinate space "'of dimensions, written "'R "'( ) ( also written with blackboard bold ) is a coordinate space that allows plane for and three-dimensional space for.
