# Scalars and determining subspaces

1. Mar 7, 2013

### MoreDrinks

To determine if a subset of a vector space is a subspace, it must be closed under addition and scalar multiplication. As far as I can tell, this means adding two arbitrary vectors in the subset and having the sum be within the subset.

But...can the scalar be any number? Is there any limitation?

2. Mar 7, 2013

### micromass

If $W$ is a subspace of $V$, then $\alpha v\in W$ for any scalar $\alpha$ and for any $w\in W$.

3. Mar 7, 2013

### MoreDrinks

Thanks, my book is terrible.