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If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...

Weak convergence is usually either denoted x_nw; ->x or x_n->x. A sequence {x_n} of vectors in an inner product space E is called weakly convergent to a vector in E if ...

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

An expression is called "well-defined" (or "unambiguous") if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to not be ...

When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

For |z|<1, product_(k=1)^infty(1+z^k)=product_(k=1)^infty(1-z^(2k-1))^(-1). (1) Both of these have closed form representation 1/2(-1;z)_infty, (2) where (a;q)_infty is a ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

Given relatively prime integers p and q (i.e., (p,q)=1), the Dedekind sum is defined by s(p,q)=sum_(i=1)^q((i/q))(((pi)/q)), (1) where ((x))={x-|_x_|-1/2 x not in Z; 0 x in ...