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.
![](https://dl1.cuni.cz/pluginfile.php/1151120/mod_glossary/entry/72268/800px-3D_Vector.svg.png)
Etymology From Latin basis and Greek βάσις
Sources OED Figure from WIKIPEDIA
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