# 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!