We (somewhat perversely) defined dim(A) in Section 5.1.1 as the size of the smallest basisof a type A. This is quite annoying, since if we want to figure out the dimension of A weneed to look at all bases of A, just to make sure that we have the smallest one. Fortunately,in linear maps we don’t have to do that, because the complex numbers form a field. Wecan therefore rely on the following theorem, called the dimension theorem.