Search Results for ""

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

A projective space is a space that is invariant under the group G of all general linear homogeneous transformation in the space concerned, but not under all the ...

Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

The point on the positive ray of the normal vector at a distance rho(s), where rho is the radius of curvature. It is given by z = x+rhoN (1) = x+rho^2(dT)/(ds), (2) where N ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Then A is said to be alternative if, for all x,y in A, (x·y)·y=x·(y·y) (3) ...

Suppose that X is a vector space over the field of complex or real numbers. Then the set of all linear functionals on X forms a vector space called the algebraic conjugate ...

The directional derivative del _(u)f(x_0,y_0,z_0) is the rate at which the function f(x,y,z) changes at a point (x_0,y_0,z_0) in the direction u. It is a vector form of the ...

A two-component complex column vector. Spinors can describe both bosons and fermions, while tensors can describe only bosons.

A linear functional on a real vector space V is a function T:V->R, which satisfies the following properties. 1. T(v+w)=T(v)+T(w), and 2. T(alphav)=alphaT(v). When V is a ...