Does a linear mapping imply that it is also bijective? I would assume this is not true because there wouldn't be a subcategory of linear mappings called bijective linear mappings then (isomorphisms, etc.). Can someone give me an example of a linear mapping that is not bijective? I keep thinking in terms of R squared and how a line obviously shows it's one-to-one and onto, and I can't think of an example where a linear mapping isn't bijective. I'm probably missing something obvious.