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A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ...

A knot K embedded in R^3=C_z×R_t, where the three-dimensional space R^3 is represented as a direct product of a complex line C with coordinate z and a real line R with ...

If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. ...

A set considered together with the sigma-algebra on the set.

Informally, a symplectic map is a map which preserves the sum of areas projected onto the set of (p_i,q_i) planes. It is the generalization of an area-preserving map. ...

Given a vector space V, its projectivization P(V), sometimes written P(V-0), is the set of equivalence classes x∼lambdax for any lambda!=0 in V-0. For example, complex ...

The set of all points x that can be put into one-to-one correspondence with sets of essentially distinct values of five homogeneous coordinates x_0:x_1:x_2:x_3:x_4, not all ...

The line segment connecting opposite polyhedron vertices (i.e., two polyhedron vertices which do not share a common face) in a parallelepiped or other similar solid. Also ...

The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...