请输入您要查询的字词:

 

单词 LinearManifold
释义

linear manifold


DefinitionSuppose V is a vector spaceMathworldPlanetmath and suppose that L is anon-empty subset of V. If there exists a vV such that L+v={v+llL}is a vector subspace of V, then L is a linear manifold of V. Then wesay that the dimensionPlanetmathPlanetmathPlanetmath of L is the dimension of L+v and write dimL=dim(L+v).In the important case dimL=dimV-1, L is called a hyperplane.

A linear manifold is, in other words, a linear subspace that has possibly beenshifted away from the origin.For instance, in 2 examples of linearmanifolds are points, lines (which are hyperplanes), and 2 itself.In n hyperplanes naturally describe tangent planes to a smoothhyper surface.

References

  • 1 R. Cristescu, Topological vector spacesMathworldPlanetmath,Noordhoff International Publishing, 1977.
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 12:24:29