Linear Algebra book recommendation ( with rigorous proofs and pure mathematical )

Question

I know, that there are a similar topics of my question, but I didn't find the answer.)

$\textbf{Problem:}$ I need a book of LA for self-study, but I want to find the book like "Introduction to real analysis by G. Bartle, R. Sherbert" in analysis, but for LA. So I mean, it has to start from basic things, but with rigorous proofs and be PURE mathematical.

$\textbf{What I tried:}$ I chosed 3 books, which I found on this forum:

1. Linear Algebra Done Right by Sheldon Axler
2. Linear Algebra. A Modern Introduction" by David Poole
3. Linear Algebra and Its Applications, 4th Edition by Gilbert Strang.

I started with the first one and I didn't like it, because this book is not precise as for me. ( In the first chapter author says: we will use $F$ for field, but it's ok, if u don't know, what field is, because if we write $F$, we mean $\mathbb R$ or $\mathbb C$ instead of define the field. I don't find it good. So can somebody recommend the book from my list or maybe book, that u like and looks like what I look for) Thank you in advance

Answer 1

Halmos' Finite Dimensional Vector Spaces or Roman's Advanced Linear Algebra are both worth considering.

Answer 2

Hoffman and Kunze - Linear Algebra.

Give it a try.