Main Question or Discussion Point
Can't quite see why a one-to-one linear transformation is also onto, anyone?
In general they aren't. If the transformation is [itex]V\rightarrow W[/itex] with V,W finite dimensional, then there are three cases:Can't quite see why a one-to-one linear transformation is also onto, anyone?
I guess I was assumming the same dimension for map, i.e., map from ##\mathbb R^n \rightarrow \mathbb R^n ## or any two vector spaces of the same dimension. There are other ways of seeing this. EDIT: Mayb be more accurate to say that map T is of full rank than saying it is onto.Rank Nullity Theorem: Nullity is zero....