Search Results for ""

Also known as the first fundamental form, ds^2=g_(ab)dx^adx^b. In the principal axis frame for three dimensions, ds^2=g_(11)(dx^1)^2+g_(22)(dx^2)^2+g_(33)(dx^3)^2. At ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...

A pullback is a general categorical operation appearing in a number of mathematical contexts, sometimes going under a different name. If T:V->W is a linear transformation ...

A copositive matrix is a real n×n square matrix A=(a_(ij)) that makes the corresponding quadratic form f(x)=x^(T)Ax nonnegative for all nonnegative n-vectors x. Copositive ...

A grammar defining formal language L is a quadruple (N,T,R,S), where N is a finite set of nonterminals, T is a finite set of terminal symbols, R is a finite set of ...

A stereogram made of two pictures, one red and one blue, taken from offset positions. When the pictures are viewed through glasses with one lens of each color, the picture ...

A straightedge with markings to indicate distances. Although geometric constructions are sometimes said to be performed with a ruler and compass, the term straightedge is ...

The cup product is a product on cohomology classes. In the case of de Rham cohomology, a cohomology class can be represented by a closed form. The cup product of [alpha] and ...

Lorentzian n-space is the inner product space consisting of the vector space R^n together with the n-dimensional Lorentzian inner product. In the event that the (1,n-1) ...

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...