To echo sibling comment but make it more prominent - "Linear Algebra Done Right" is a great second book, I wouldn't use it as a first source of learning Linear

To echo sibling comment but make it more prominent - "Linear Algebra Done Right" is a great second book, I wouldn't use it as a first source of learning Linear Algebra. (I'm pretty sure it says as much in the intro, IIRC.) I personally learned from Strang, then this book, which complemented each other very well. Strang is very focused on practicality, actually computing things, always seeing the matrix behind everything. "Done Right" is great at ignoring most of the "matrix view" of things completely in favor of pure linear transformations instead. Both views have their use - so learning one, then the other, is a great idea.