Some linear algebra books try to focus on concrete geometrical intuitions (like Practical Linear Algebra: A Geometry Toolbox), from which more abstract concepts can be generalized. Others (like Linear Algebra Done Right) take a high-level approach, starting at a general level and linking abstract concepts through elegant proofs. This book does neither. For example, it defines concepts like matrix multiplication and determinant with absolutely no motivation. You might expect a chapter on determinants to contain, oh I don't know, a picture of a parallelogram somewhere? Keep looking. It spends whole chapters teaching you to perform busy-work algorithms by hand, when they could easily be automated. So you get NO insight of any kinds – either concrete geometrical insight, nor algebraic insight about the abstract relationships between the concepts.
I don't have a constructive proof for the existence of an ideal linear algebra textbook, but the proof that it exists is a simple lemma: it is exactly the complement of this one.
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