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A real-linear vector space H equipped with a symplectic form s.

The Lorentz group is the group L of time-preserving linear isometries of Minkowski space R^((3,1)) with the Minkowski metric dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2 ...

The word basis can arise in several different contexts. Speaking in general terms, an object is "generated" by a basis in whatever manner is appropriate. For example, a ...

An action with G=R. Flows are generated by vector fields and vice versa.

The kernel of a linear transformation T:V-->W between vector spaces is its null space.

A special case of a flag manifold. A Grassmann manifold is a certain collection of vector subspaces of a vector space. In particular, g_(n,k) is the Grassmann manifold of ...

The upside-down capital delta symbol del , also called "nabla" used to denote the gradient and other vector derivatives. The following table summarizes the names and ...

The upside-down capital delta symbol del , also called "del," used to denote the gradient and other vector derivatives. The following table summarizes the names and notations ...

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product a·b=0. (1) In ...

A basis for the real numbers R, considered as a vector space over the rationals Q, i.e., a set of real numbers {U_alpha} such that every real number beta has a unique ...