When applied to
vector spaces in
mathematics,
Hamel basis means the same thing as ordinary or algebraic
basis. That is, a
Hamel basis of a
vector space V is a
linearly independent set B of
elements of V, such that every
element of V is a
finite linear combination of
elements of B.
The term Hamel basis emphasizes that, even if V is infinite-dimensional, we insist that every element of V be a finite linear combination of elements of B. When dealing with infinite-dimensional vector spaces, for instance in functional analysis, one frequently calls a set B a basis for V when the set of all finite linear combinations of elements of B is merely dense in V. For applications to analysis this approximation property is more natural. See orthonormal basis.