I'm currently going through a book called Linear Algebra Done Right by Axler, and to be honest, his book seems to be very loose with what things he defines. For instance , the symbol 0 could be mean a zero vector or a scalar. Not only on defining things , but the proofs as well are also loose. I feel like this book is not meant for the beginner like myself who wants to jump into learning the theory behind linear algebra. It feels more like a book for reviewing or brushing upon your linear algebra skills.
In any case, I find that I learn best when doing proofs is to translate the statements in terms of quantifiers and connectives. In short, I don't want to go dissect all the flowery language. I just want to cut to the chase. So, are there any books that's presented in this manner that I described?