Definition
A set of vectors are said to be linearly independent if there exist no non-trivial linear combinations of equal to the zero vector.
Remark
We say the empty list is linearly independent.
A set of vectors v1,v2,…,vn∈V are said to be linearly independent if there exist no non-trivial linear combinations of v1,v2,…,vn equal to the zero vector.
We say the empty list is linearly independent.