Question for those who have studied Roman's book "Advanced Linear Algebra". How self-contained is this book. Can I study determinants directly from this in context of exterior algebra and tensor products?
How much one can understand if he didn't have a previous course in Linear Algebra.
I want to study linear algebra but I want to do it properly with focus in abstract algebra. That is, I want the book to talk about modules, tensor products, exterior algebras.
I tried Blyth's "Module theory - an approach to linear algebra" and Winitzki's "Linear Algebra via Exterior Products", but it didn't work out very well. Not beause the material was too hard, but because I simply don't like the style. It's not fully rigorous. Now I hope I can learn something from Roman's book.
Well I think the book is quite self-contained. Probably you won’t need to take a pre-course when studying the book since the book has covered the topics quite rigorously and explicitly.
For example, chapter $0$ covers the topics on some basic cardinal arithmetic and the author immediately applies it in the proof of some dimension equations in chapter $1$.
And comments in the book provide an insight into the definition which is appreciated by me. See for example in tensors.