Basis

Noun
Plural: bases

Pronunciation
/'beɪsɪs/ listen

Meaning
A basis is a set of vectors that generates all elements of the vector space and the vectors in the set are linearly independent.
More formally: Let V be a vector space over a fieldF. A subset M which generates the vector space V and which is a linearly independent subset is called a basis of vector space V.
The subset M satisfies the linear independence property and the spanning property.

Examples
Canonical basis {e1, e2, ... en} in F n

The figure shows the basis vectors i,j, k, and the vector a is a linear combination of them.



Etymology
From Latin basis and Greek βάσις

Sources
OED
Figure from WIKIPEDIA

 

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