Looking for guidance to study linear algebra As the title implies, I'm in need of some guidance from people with experience in linear algebra on how I should approach the subject to learn more effectively.
My background:
I'm a masters student in computer science working with theoretical stuff that involves lots of linear algebra. Before the masters, my education in mathematics was, to be honest, terrible. Fortunately, I have being able to keep up and have taught myself a fair amount of discrete mathematics. As a result, today I feel much more comfortable with proof writing (or the so called mathematical maturity). Now, the quest is to learn linear algebra.
My goal:
Learn (or master, if possible) linear algebra until the end of this year. I need to learn well at least the basics (up to orthogonality, projection matrices, etc) until September. Although I'm not a beginner in the subject, I'm very far from proficient. I'm interested in learning linear algebra for further studies in theoretical computer science, e.g. algorithms, graph theory, combinatorial optimization, etc. Let me make some points clear:

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*I don't work with numerical linear algebra, and don't intend to.

*I'm NOT interested in learning linear algebra for machine learning and/or computer graphics (although I find ML interesting..). Just saying because people in CS usually associate linear algebra with these subjects.

*I'm looking to improve my mathematical maturity, so a proof-based approach to learn linear algebra is very welcome.

My resources:
I have at my disposal three books: Axler's Linear Algebra Done Right, Strang's Introduction to Linear Algebra, and Schaum's Outline of Linear Algebra. A while ago, I started reading Axler's and found it very interesting, but I didn't even finish chapter 1 because I have some concerns lurking in my head. I feel I'm skipping steps and jumping right into an advanced book. Here are my concerns about each book:

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*Strang: as far as I could see, the book deals almost exclusively with matrices and applications. Vector spaces are treated with less rigor, and linear transformations appear in a brief chapter towards the end of the book. Although I think the appeal for intuition seems nice, the lack of rigor in many parts bothers me a lot. I feel I'd be missing important details. In addition, the book is filled with applications that don't interest me at all (e.g. differential equations, circuits, networks, etc). A huge plus is the online lectures though. What worries me the most is the lack of rigor (no proofs) and emphasis in applications that don't interest me.

*Axler: beautifully written and very readable, with extensive treatment of vector spaces, linear transformations, etc. However, I saw almost no matrix algebra and some topics seem very out of my context (e.g. vector space of polynomials). Nevertheless, I genuinely find the book very interesting, but at this moment I have to make pragmatic decisions and leave less useful stuff to be seen later. A huge plus of this book is that I'd have the opportunity to improve my proof-writing skills and lay a solid foundation. What worries me the most is the absence of matrix algebra.

*Schaum: just a reference with a bunch of exercises. Don't know if it's sufficient by itself. I thought in coupling this one with Axler's.

It's like Axler and Strang are two extremes, one treating something the other does not. Strang starts with systems of linear equation with those endless and boring mechanical calculations, but seems to have an extensive treatment of matrix algebra. On the other hand, Axler jumps right into the interesting stuff (vector spaces), but has almost nothing about matrices.
The ideal approach, of course, would be to read both in sequence. But I'm afraid time will not be my friend here and (forgive me for the drama) I'm desperate to learn this subject. Nevertheless, if it's really worth the time and there's no better way, I think I'd be able to manage it. Do you think it'd be worth it? Should I look for another text that has the best of both worlds? Or maybe you have alternative suggestions that would be more effective?
 A: Hoffman Kunze's is a good book.I highly recommend this book.Axler's book   doesn't cover the all syllabus of linear Algebra. Axler skipped many important topics of linear Algebra.It's easy to waste time with a poorly written textbook.
"Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty"- Archimedes
Mathematics is not a competitive sport -Grothendieck
It’s also good to remember that professional mathematics is not a sport (in sharp contrast to mathematics competitions). The objective in mathematics is not to obtain the highest ranking, the highest “score”, or the highest number of prizes and awards; instead, it is to increase understanding of mathematics (both for yourself, and for your colleagues and students), and to contribute to its development and applications. For these tasks, mathematics needs all the good people it can get.- Terence Tao
A: Based on your remarks, I'd say make your focus Axler, or some other similarly theoretical book, and spend $\textit{some}$ time studying the matrix stuff if you feel you need more (I don't know to what extent matrix computations are important for your work). Alternatively, you can first skim through Strang to remind yourself of the subject or acquaint yourself with the basics, and then begin the more serious treatment of Axler. But the bulk should undoubtedly (in my humble opinion) be from a book similar in character to Axler. Linear algebra isn't about matrices, it's about (finite-dimensional) vector spaces and linear transformations. The matrix computations you can, after a certain foundational understanding, just pick up real quick when you need them. You can't just pick up a solid understanding of vector spaces real quick.
