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Let x be a point in an n-dimensional compact manifold M, and attach at x a copy of R^n tangential to M. The resulting structure is called the tangent space of M at x and is ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

A term of endearment used by algebraic topologists when talking about their favorite power tools such as Abelian groups, bundles, homology groups, homotopy groups, K-theory, ...

A vector space possessing a norm.

A change of basis is the transformation of coordinate-based vector and operator representations in a given vector space from one vector basis representation to another.

A vector norm defined for a vector x=[x_1; x_2; |; x_n], with complex entries by |x|_infty=max_(i)|x_i|. The vector norm |x|_infty of the vector x is implemented in the ...

The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...

The direction from an object A to another object B can be specified as a vector v=AB^-> with tail at A and head at B. However, since this vector has length equal to the ...

C=tauT+kappaB, where tau is the torsion, kappa is the curvature, T is the tangent vector, and B is the binormal vector.

A vector field v for which the curl vanishes, del xv=0.