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A real vector bundle pi:E->M has an orientation if there exists a covering by trivializations U_i×R^k such that the transition functions are vector space ...

A bra <psi| is a vector living in a dual vector space to that containing kets |psi>. Bras and kets are commonly encountered in quantum mechanics. Bras and kets can be ...

The angle of incidence of a ray to a surface is measured as the difference in angle between the ray and the normal vector of the surface at the point of intersection.

Two curves which, at any point, have a common principal normal vector are called Bertrand curves. The product of the torsions of Bertrand curves is a constant.

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

The comass of a differential p-form phi is the largest value of phi on a p vector of p-volume one, sup_(v in ^ ^pTM,|v|=1)|phi(v)|.

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

The cotangent bundle of a manifold is similar to the tangent bundle, except that it is the set (x,f) where x in M and f is a dual vector in the tangent space to x in M. The ...

One of the "knots" t_(p+1), ..., t_(m-p-1) of a B-spline with control points P_0, ..., P_n and knot vector T={t_0,t_1,...,t_m}, where p=m-n-1.

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.