Search Results for ""

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

A genetic algorithm is a class of adaptive stochastic optimization algorithms involving search and optimization. Genetic algorithms were first used by Holland (1975). The ...

Let A be an n×n real square matrix with n>=2 such that |sum_(i=1)^nsum_(j=1)^na_(ij)s_it_j|<=1 (1) for all real numbers s_1, s_2, ..., s_n and t_1, t_2, ..., t_n such that ...

A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological ...

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

The space B of a fiber bundle given by the map f:E->B, where E is the total space of the fiber bundle.