What exactly does it mean for two points to be barycentrically independent?

1. Dec 5, 2011

Mathguy15

Hello, I've been studying some linear algebra, and i am stuck on a certain definition.
The book i am using says that points{p0,p1,...,pk} in a vector space V are barycentrically independent if and only if the vectors {p1-p0,p2-p0,...,pk-p0} are linearly independent. The problem i have is the definition for two points. The definition in the book seems to work only for k≥2, but what about k=1? I'm sorry if I am missing something completely obvious, and i'll check more carefully if this is the case.

Sincerely,
mathguy15

2. Dec 5, 2011

Office_Shredder

Staff Emeritus
Two (distinct) points are automatically barycentrically independent, in the same way that a single (nonzero) point in automatically linearly independent

3. Dec 5, 2011

Mathguy15

so two points are barycentrically independent if and only if the vector they form is nonzero?

4. Dec 5, 2011

micromass

Staff Emeritus
Yes!

5. Dec 5, 2011

Thanks!