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Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

If V and W are Banach spaces and T:V->W is a bounded linear operator, the T is said to be a compact operator if it maps the unit ball of V into a relatively compact subset of ...

The Fibonacci Q-matrix is the matrix defined by Q=[F_2 F_1; F_1 F_0]=[1 1; 1 0], (1) where F_n is a Fibonacci number. Then Q^n=[F_(n+1) F_n; F_n F_(n-1)] (2) (Honsberger ...

A manifold with a Riemannian metric that has zero curvature is a flat manifold. The basic example is Euclidean space with the usual metric ds^2=sum_(i)dx_i^2. In fact, any ...

A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...

A number which is simultaneously a heptagonal number H_n and square number S_m. Such numbers exist when 1/2n(5n-3)=m^2. (1) Completing the square and rearranging gives ...

A number which is simultaneously a heptagonal number H_n and triangular number T_m. Such numbers exist when 1/2n(5n-3)=1/2m(m+1). (1) Completing the square and rearranging ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

There are several different definition of link. In knot theory, a link is one or more disjointly embedded circles in three-space. More informally, a link is an assembly of ...

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...