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linear combination (Definition)

A linear combination of vectors $ \vec{v}_1,\dots,\vec{v}_n$ of a vector space $ V$ over a field $ F$ is a vector of the form

$\displaystyle \sum_{i=1}^n a_i\vec{v}_i,$
where the $ a_i$ are elements of $ F$.



"linear combination" is owned by yark. [ full author list (2) | owner history (1) ]
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Keywords:  linear combination, span
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Cross-references: field, vector space, vectors
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This is version 12 of linear combination, born on 2001-11-13, modified 2004-04-05.
Object id is 805, canonical name is LinearCombination.
Accessed 13463 times total.

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