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A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthonormal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. ...

The coordinates representing any point of an n-dimensional affine space A by an n-tuple of real numbers, thus establishing a one-to-one correspondence between A and R^n. If V ...

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 ...

Two vector bundles are stably equivalent iff isomorphic vector bundles are obtained upon Whitney summing each vector bundle with a trivial vector bundle.

Given a vector bundle pi:E->M, its dual bundle is a vector bundle pi^*:E^*->M. The fiber bundle of E^* over a point p in M is the dual vector space to the fiber of E.

An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

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.

A vector field on a circle in which the directions of the vectors are all at the same angle to the circle.