# Vector spaces

1. Jan 29, 2009

### garyljc

Just have a question
if U,V and W are over the same field K
does it mean that dim U = dim V = dim W ?

2. Jan 29, 2009

### Ben Niehoff

No.

For example, $R^2$ and $R^3$ are both over the same field R, but R^2 has dimension 2 and R^3 has dimension 3.