A Hamel basis (often simply called basis) of a vector space $V$ over a field $F$ is a linearly independent subset of $V$ that spans it.

A Hamel basis (often simply called basis) of a vector space $V$ over a field $F$ is a linearly independent subset of $V$ that spans it. In other words, a subset $B$ of $V$ is a basis when every element of $V$ can be expressed in one and only one way as a (finite) linear combinations of elements of $B$. It can be proved that all bases of a vector space have the same cardinal, which is (by definition) the dimension of $V$.

The term "Hamel basis" is used mostly in reference to vector spaces of infinite dimension, where other notions of bases are used.