The vector space span of a subset 
of a vector space 
over a field 
is the set of all finite linear combinations of vectors
in 
. It is the smallest subspace
of 
containing 
. For 
,
 |
For an infinite set 
, each individual linear
combination still uses only finitely many vectors.
The span of the empty set is 
(Axler 2024, pp. 28-29).
For example, the span of two vectors 
and 
in a real vector space 
is the subspace
 |
A set of vectors 
can be tested to see if they form a spanning
set of 
-dimensional
space using the following Wolfram Language
function:
SpanningVectorsQ[m_List?MatrixQ] :=
(NullSpace[m] == {})
