If the null space of a set is equal to just the zero vector, whats the nullity of that set? 0?

2/26/2007 8:53:51 PM

I think you mean null space of a "vector space / subspace" or possibly the span of a *set/collection of vectors.

Anyway, semantics aside, the answer is yes.

If the null space is just the zero vector, then it's nullity is zero. Think about rank+nullity. If the subspace only has a trivial nullspace then it spans the whole space, hence it has full rank and so the nullity must be zero.

[Edited on February 26, 2007 at 10:34 PM. Reason : .]

2/26/2007 10:28:21 PM

extremely helpful, thanks man.

2/27/2007 6:58:15 PM