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definition in linear algebra
''Basis is a [[mathematics]] term.''
''Basis is a [[mathematics]] term.''
== Linear algebra ==
In [[linear algebra]], a basis is a set of [[linearly independent]] vectors that [[spans]] a vector space. Any vector in the vector space can then be written as a linear combination of the basis.
This usage of the term is similar to its common usage: a basis is the foundation for what is needed.
== Topology ==
A '''basis''' ''B'' for a [[topology]] ''T'' on a set ''X'' is a collection of subsets of ''X'' (called '''basis elements''') such that
A '''basis''' ''B'' for a [[topology]] ''T'' on a set ''X'' is a collection of subsets of ''X'' (called '''basis elements''') such that