Span, Basis, and Dimensions
Learn the concepts of the span, the dimension of a vector space, and the basis of a vector space.
Span
The span of a set, , is another set, , consisting of all the linear combinations of vectors in . The set is referred to as a spanning set.
Examples
We can create any vector in , say , using a linear combination of the spanning set . So, spans . That is:
- line in the direction of
Note: A line consists of points that are also position-vectors.
Spanning set isn’t unique
A spanning set corresponding to a given span isn’t unique.
In a previous example, we showed that . . However, there exists infinitely many spanning sets that span ...