Resources for learning how to do proofs Linear algebra

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Resources for learning proofs in linear algebra include "Principles of Mathematics" by Allendoerfer and Oakley, and "Geometry" by Harold Jacobs (not the third edition). Many find these foundational texts helpful for understanding abstract math concepts. Additionally, "Discrete Mathematics Demystified" and "Euclidean Geometry: A First Course" by Mark Solomonovich are recommended for their clarity. Engaging with these materials can enhance comprehension of proof techniques more effectively than some dedicated proof-focused books. Mastery of these resources can significantly improve one's ability to tackle proof questions in linear algebra.
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Any resources to learn how to do proofs or view abstract math better in linear algebra?

A lot of time when I read the solution to proof questions, I don't even see how that proves the statement. The way they are written seems unintuitive. This is my first abstract math course. I've never had so much trouble in a course before. The are computations are easy though at least.
 
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linear algebra is often used as the first proofs course. It helped me however to have a prior course just on the idea of a proof in general. I learned from the first few chapters of principles of mathematics by allendoerfer and oakley. another good introduction is in the first or possibly second edition of geometry by harold jacobs, but not the third edition. other books on proofs people like are velleman, etc but i do not like many of them much myself.
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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