Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon: Annotation to

Basis

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview
A subset $ B$ of vector space $ V$ is called basis of $ V$, if $ B$ is linearly independent as well as a generating system for $ V$, that is, any vector $ v\in V$ has a unique representation as finite linear combination

$\displaystyle v = \sum_{i=1}^n \lambda_i b_i $

where $ b_i\in B$.

In a finite-dimensional vector space any vector can be described by its coordinates relative to a given basis:

$\displaystyle v_B = (\lambda_1,\ldots,\lambda_n)^{\operatorname t}\,. $

In an infinite-dimensional vectorspace a generating system $ S$ is a basis if and only if any finite subset of $ S$ consists of linearly independent vectors.

(temporary unavailable)
[Back]
  automatisch erstellt am 19.  8. 2013