Thread: Linear Algebra Texts, the end all, be all

Which texts in linear algebra are considered to be the best from a mathematical point of view, (i.e. in terms of presentation, clarity, rigour, difficulty)?

I would like suggestions for an introductory book on the subject as well as a second treatment for undergraduates. Is there also an "introductory" graduate level text that you could recommend?

I liked W. Keith Nicholson. It was the text for Linear Algebra at Grove City College, the best course I took there. It's a good intro at the undergraduate level. Some might prefer Linear Algebra Done Right, by Axler. I'm not sure of graduate level texts on the subject. A course in numerical analysis will have a good bit of advanced linear algebra in it. I recommend Burden and Faires for that subject.

For a more second treatment I would suggest Finite-Dimensional Vector Spaces by Paul Halmos