“Grassmannian”的概念、定义、习题解题方法及翻译-数学辞典

单词

Grassmannian

释义

Grassmannian

The Grassmannian G(k,n), named after Hermann Grassmann (1809–77), is a smooth manifold parameterizing all the k-dimensional subspaces of Rn. When k = 1, this is (n–1)-dimensional real projective space. When k = 2, a subspace can be determined by a basis v1,v2. Unfortunately, there are many different bases for the same subspace. However, if ∧ denotes the exterior product, then

and so any two bases give the same product in ⋀2Rn up to a scalar multiple. This means that G(2,n) can be considered as a submanifold of the projective space ℙ(⋀2Rn) and more generally G(k,n) ⊆ ℙ(⋀^kRn). The dimension of G(k,n) equals k(n−k).

随便看

数学辞典收录了4151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。