Definitions
A vector is redundant if: This means it can be omitted in the vector space.
Example
The vector is redundant as so can be constructed as a Linear Combination of and
A vector w∈{w,v1,…,vk} is redundant if: span(w,v1,…,vk)=span(v1,…,vk) This means it can be omitted in the vector space.
The vector (1,2)∈{(1,2),(1,0),(0,1)} is redundant as (1)(1,0)+(2)(0,1)=(1,2)∈span((1,2),(1,0),(0,1)) so (1,2) can be constructed as a Linear Combination of (1,0) and (0,1)