Hi, I have to take a placement exam in linear algebra this fall so I have been studying some past exams. This is a real basic question. If we have a linear transformation T:W -> W does this imply nothing about the injectivity or surjectivity of the transformation? I assume that it does not, but I get confused because if it is not surjective, then it seems like the image of T is not W but some subspace of W. To phrase it in a different way, does T: W -> W only say that T maps vectors in W to other vectors in W and nothing about what the image in W is? Thanks!