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A theorem which specifies the structure of the generic unitary representation of the Weyl relations and thus establishes the equivalence of Heisenberg's matrix mechanics and ...

Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for ...

To each epsilon>0, there corresponds a delta such that ||f-g||<epsilon whenever ||f||=||g||=1 and ||(f+g)/2||>1-delta. This is a geometric property of the unit sphere of ...

The span of subspace generated by vectors v_1 and v_2 in V is Span(v_1,v_2)={rv_1+sv_2:r,s in R}. A set of vectors m={v_1,...,v_n} can be tested to see if they span ...

The Banach-Saks theorem is a result in functional analysis which proves the existence of a "nicely-convergent" subsequence for any sequence {f_n}={f_n}_(n in Z^*) of ...

A category consists of three things: a collection of objects, for each pair of objects a collection of morphisms (sometimes call "arrows") from one to another, and a binary ...

Analysis

The 57-cell, also called the pentacontaheptachoron, is a regular self-dual locally projective polytope with 57 hemidodecahedral facets described by Coxeter (1982) and also ...

Let P be the set of prime ideals of a commutative ring A. Then an affine scheme is a technical mathematical object defined as the ring spectrum sigma(A) of P, regarded as a ...

A barrel solid of revolution composed of parallel circular top and bottom with a common axis and a side formed by a smooth curve symmetrical about the midplane. The term also ...