We have $n$ vectors each with $k$ components. Let $V$ be their span and $r$ be the dimension of $V$. Then $r \leq k$.
I encountered this in a paper I am reading. I am not able to see why this is true(probably due to my not so sound linear algebra background).
Can anyone help me in understanding why the argument is true? Thanks.
Link to paper: https://www.cs.tau.ac.il/~shpilka/publications/RazShpilka_PIT.pdf