Search results
Results from the WOW.Com Content Network
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
exponential map (Lie theory) from a Lie algebra to a Lie group, More generally, in a manifold with an affine connection , X ↦ γ X ( 1 ) {\displaystyle X\mapsto \gamma _{X}(1)} , where γ X {\displaystyle \gamma _{X}} is a geodesic with initial velocity X , is sometimes also called the exponential map.
Globally, the exponential map is not necessarily surjective. Furthermore, the exponential map may not be a local diffeomorphism at all points. For example, the exponential map from (3) to SO(3) is not a local diffeomorphism; see also cut locus on this failure. See derivative of the exponential map for more information.
The exponential map of the Earth as viewed from the north pole is the polar azimuthal equidistant projection in cartography. In Riemannian geometry, an exponential map is a map from a subset of a tangent space T p M of a Riemannian manifold (or pseudo-Riemannian manifold) M to M itself. The (pseudo) Riemannian metric determines a canonical ...
The matrix exponential then gives us a map : (,) from the space of all n×n matrices to the general linear group of degree n, i.e. the group of all n×n invertible matrices. In fact, this map is surjective which means that every invertible matrix can be written as the exponential of some other matrix [ 9 ] (for this, it is essential to consider ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
A field is an algebraic structure composed of a set of elements, F, two binary operations, addition (+) such that F forms an abelian group with identity 0 F and multiplication (·), such that F excluding 0 F forms an abelian group under multiplication with identity 1 F, and such that multiplication is distributive over addition, that is for any elements a, b, c in F, one has a · (b + c) = (a ...
The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and ...