This is a general question because I don't seem to be getting a straight answer from my textbook. I know how to find eigenvalues/vectors, but finding IF an eigenbasis exists is what is throwing me off. Can someone give me an example of, say, a 3x3 matrix and go through the procedure of finding if the basis exists and then how to find it? I know this is probably asking a lot, but I am confused! Any help would be much appreciated.