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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 ...

A four-vector a_mu is said to be lightlike if its four-vector norm satisfies a_mua^mu=0. One should note that the four-vector norm is nothing more than a special case of the ...

Let |z| be a vector norm of a vector z such that ||A||=max_(|z|=1)||Az||. Then ||A|| is a matrix norm which is said to be the natural norm induced (or subordinate) to the ...

A four-vector a_mu is said to be spacelike if its four-vector norm satisfies a_mua^mu>0. One should note that the four-vector norm is nothing more than a special case of the ...

A four-vector a_mu is said to be timelike if its four-vector norm satisfies a_mua^mu<0. One should note that the four-vector norm is nothing more than a special case of the ...

Tracing through the connections of a branchial graph gives rise to the notion of a kind of space in which states on different branches of history are laid out. In particular, ...

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.