PlanetMath: standard basis

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standard basis

(Definition)

If is a division ring, then the direct sum of copies of ,

$\displaystyle R^n = R \oplus\dotsb\oplus R$ (n times),

The standard basis for consists of elements

$\displaystyle e_1 = (1,0,\dotsc ,0), \quad e_2 = (0,1,0,\dotsc ,0),\quad \dotsc \quad e_n = (0,\dotsc ,0,1)$

where each

has

for its

th component and 0 for every other component. The

are called the standard basis vectors.

"standard basis" is owned by Mathprof. [ full author list (2) | owner history (1) ]

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Also defines:

standard basis vectors

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Cross-references: vector space, division ring
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This is version 6 of standard basis, born on 2004-04-26, modified 2007-10-31.
Object id is 5806, canonical name is StandardBasis.
Accessed 5669 times total.

Classification:

15A03 (Linear and multilinear algebra; matrix theory :: Vector spaces, linear dependence, rank)

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