Real coordinate space - Wikipedia

Real coordinate space - Wikipedia: "it is the prototypical real vector space and is a frequently used representation of Euclidean n-space."



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Euclidean space - Wikipedia

Euclidean space - Wikipedia: "A Euclidean space is not technically a vector space but rather an affine space,"



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Unit sphere - Wikipedia

Unit sphere - Wikipedia: " forms[edit source]
If V is a linear space with a real quadratic form F:V → R, then { p ∈ V : F(p) = 1 } may be called the unit sphere[1][2] or unit quasi-sphere of V."



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Orthogonal group - Wikipedia

Orthogonal group - Wikipedia: "The term "orthogonal group" may also refer to a generalization of the above case: the group of invertible linear operators that preserve a non-degenerate symmetric bilinear form or quadratic form[1] on a vector space over a field. In particular, when the bilinear form is the scalar product on the vector space F n of dimension n over a field F, with quadratic form the sum of squares, then the corresponding orthogonal group, denoted O(n, F ), "



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Symmetry group - Wikipedia

Symmetry group - Wikipedia: "The proper symmetry group is then a subgroup of the special orthogonal group SO(n), and is therefore also called rotation group of the figure."



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Symmetry group - Wikipedia

Symmetry group - Wikipedia: "The proper symmetry group of an object is equal to its full symmetry group if and only if the object is chiral (and thus there are no orientation-reversing isometries under which it is invariant)."



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Symmetry group - Wikipedia

Symmetry group - Wikipedia: "The proper symmetry group of an object is equal to its full symmetry group if and only if the object is chiral (and thus there are no orientation-reversing isometries under which it is invariant)."



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