Search Results for ""

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (Sigma), it is used as a symbol for sums and series. As a lower case letter (sigma) it ...

A Kähler structure on a complex manifold M combines a Riemannian metric on the underlying real manifold with the complex structure. Such a structure brings together geometry ...

The conical spiral with angular frequency a on a cone of height h and radius r is a space curve given by the parametric equations x = (h-z)/hrcos(az) (1) y = (h-z)/hrsin(az) ...

An experiment E(S,F,P) is defined (Papoulis 1984, p. 30) as a mathematical object consisting of the following elements. 1. A set S (the probability space) of elements. 2. A ...

For any function f:A->B (where A and B are any sets), the kernel (also called the null space) is defined by Ker(f)={x:x in Asuch thatf(x)=0}, so the kernel gives the elements ...

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...

A bounded linear operator T in B(H) on a Hilbert space H is said to be cyclic if there exists some vector v in H for which the set of orbits ...

Given an open subset U in n-dimensional space and two compact subsets C_0 and C_1 of U, where C_1 is derived from C_0 by a continuous motion, is it possible to move C_0 to ...

If M^n is a finite simplicial complex of dimension n>=5 that has the homotopy type of the sphere S^n and is locally piecewise linearly homeomorphic to the Euclidean space ...