Once the dimension of a vector space is known, then the determination of whether or not a set of vectors is linearly independent, or if it spans the vector space, can often be much easier. In this section we will state a workhorse theorem and then apply it to the column space and row space of a matrix. It will also help us describe a super-basis for \(\complex{m}\text{.}\)

- License
- GFDL-1.2
- Submitted At
- September 11th, 2017
- 7 years ago
- Views
- 2
- Type
- Language
- English
- Content Type
- text/html

##### A set of vectors containing more elements than the dimension of the space must be linearly dependent, arbitrary vector space. math.la.t.vsp.dim.more.lindep.arb

##### math.la.t.vsp.dim.less.span.arb

##### math.la.t.vsp.dim.span.linindep.arb