Linear algebra MOC

Basis of a vector space

Given a Vector space , a (Hammel) basis is a linearly independent spanning set of .¹ linalg A basis is particularly useful in the form of an Ordered basis, allowing for vectors and linear maps to be represented as coördinate matrices.

Basis proofs

To prove that a set is a basis for the space , it is necessary to show the following:

2. is linearly dependent

See also Dense basis.

Properties

1. Every vector space has a basis

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Footnotes

1. 2008. Advanced Linear Algebra, p. 47 ↩