I recently took an introductory class on linear algebra (covered solving linear systems, determinants, eigenvectors, diagonalization, some vector spaces, basis and combinations, transformations etc.)
Since it was a class for engineering students, it was mostly going through the motions without any insight - felt very mechanical and repetitive. However, I want to get a deeper understanding of the material, how it relates to vector spaces, geometry etc. For this I'd like a textbook recommendation.
Keep in mind I'm just a second-year undergraduate in engineering, so something rigorous might go over my head. Thanks!
I personally do not think it is ideal to try to learn linear algebra from one text. My personal favorite text is the one by Gilbert Strang. It is very good at the conceptual aspects of the subject, and in particular focuses on abstract topics starting as early as chapter 2. By contrast, the main other text that I am familiar with, by David Lay, sticks to essentially computational topics until chapter 4 (although to be fair chapter 3 is rather short).
The downside to this is obvious: Strang's treatment of the basics, while well-written, is relatively terse. As a result, I think most students will struggle if they start with Strang. So I would suggest starting with another text (I really don't have a recommendation; I found Lay's book adequate but not excellent) and then moving on to Strang when you have grasped the basics.
I especially think Strang would ultimately be good for you in particular because you mention that you want more explanation rather than conciseness. Strang definitely provides that, with a lot of expository paragraphs in each chapter (except the first).