Definition
The set of all possible linear combinations of a list of vectors is called the span of and denoted .
The span of the empty list is .
If , we say that spans .
Properties
- is the smallest subspace of that contains all of .
The set of all possible linear combinations of a list of vectors v1,v2,…,vm∈V is called the span of v1,…,vm and denoted span(v1,…,vm).
The span of the empty list is {0}.
If V=span(v1,…,vm), we say that v1,…,vm spans V.