I am taking an undergraduate course in computer science an is in the first year of my college. I like mathematics and am willing to learn Linear Algebra first and then move on to Abstract Algebra and further into Topology ,Computational Geometry and other parts like Number Theory,Probability and Discrete Mathematics.
Now my friend in an undergraduate course in Mathematics told me that their professor has recommended "Finite Dimensional vector Spaces" by Halmos for the first course in Algebra. I found that book to be a bit tough. So I coupled it with Sheldon Axler's "Linear Algebra done Right" looking for more basic explanations or background knowledge. But my friend says that he has heard that Axler's book is not good and lacks in providing proper concept.
Which book is going to be good for backing up Halmos. It is not that I am unable to understand. But I feel that I need more background knowledge. Which book should I read to get that background knowledge. Am I doing things wrong ? Should I restart learning Linear Algebra from the beginning ?
I am a pretty much beginner in abstract mathematics. Please help.