standard basis

If $R$ is a division ring, then the direct sum (http://planetmath.org/DirectSum) of $n$ copies of $R$ ,

R^{n}=R\\oplus\\cdots\\oplus R\\text{ (n times),}

is a vector space.

The standard basis for $R^{n}$ consists of $n$ elements

e_{1}=(1,0,\\ldots,0),\\quad e_{2}=(0,1,0,\\ldots,0),\\quad\\ldots\\quad e_{n}=(0,%\\ldots,0,1)

where each $e_{i}$ has $1$ for its $i$ th component and $0$ for every other component.The $e_{i}$ are called the standard basis vectors.

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。