MATH1231 - Linear Independence

The goal of independence is determining whether we can find a spanning set for a given subspace that is 'minimal' (i.e. each 'building block' is non-redundant, or *independent*)

Linearly Dependent Example

(1 1) (2 2) can be written as (1 1) 2(1 1), and the two are hence not linearly dependent.

Linearly **In**dependent Example

(1 1) (2 3) are not dependent as one cannot be written as a scalar multiple of the other.

For S = {v1, v2, … , vn}

If we can find scalars (that aren't all zero) so that

α1v1 + α2v2 + … + αnvn = 0

then S is linearly dependent

Else if the only solution is all α being 0

then S is linearly independent

## If all the vectors are linearly independent then the dim(span{v1, v2, …, vn}) = the number of vectors.

page revision: 2, last edited: 05 Sep 2011 05:46