Hamel Basis

up:: Finitely Generated Vector Space

Let $(V,+,\cdot )$ be a finitely generated vector space, and $B\subset V$. Then $B$ is said to be a (Hamel) basis if

• $B$ Spans $V$ (by finite Linear Combinations)
• $B$ is Linearly Independent (ensures that all vectors in $V$ have a unique linear combination from $B$)

Properties

• Every finitely generated vector space has a Hamel basis
• All Hamel bases have the same number of elements (in a finitely generated vector space)
• Sets larger than a finitely generated space’s bases are linearly dependent