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Homestandard basis

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# standard basis

If $R$ is a division ring, then the direct sum 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*.

Defines:

standard basis vectors

Related:

BasalUnits

Major Section:

Reference

Type of Math Object:

Definition

Parent:

## Mathematics Subject Classification

15A03*no label found*

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