fasterik
Joined 4 years ago
Joined 4 years ago
Axler's "Linear Algebra Done Right" https://linear.axler.net/LADR4e.pdf
Nielsen and Chuang's "Quantum Computation and Information" Chapter 2. (Available online, but legality depends on where you live)
If you're interested primarily in QM rather than linear algebra, I'd recommend not working through all of Axler, but instead using Nielsen and Chuang to learn about qubits and observables, and using Axler to fill in the gaps.
As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems [1]. The math is accessible at a pre-calculus level, and the most "counter-intuitive" aspects of QM (interference, the uncertainty principle, entanglement) make perfect sense in this framework. I think it's the best starting point for understanding what QM really says.
[0] That's not to say they aren't important historically or for a complete understanding of QM. I'm talking about conceptual understanding for someone, especially an amateur, encountering QM for the first time.
[1] Chapter 2 of Nielsen and Chuang is what did it for me. It's heavygoing if you've never seen linear algebra before, but I don't know of a clearer explanation of the postulates of quantum mechanics.
Volume isn't really a problem going forward, at least in mathematics, since every proof can be accompanied by a Lean verification. Whether other disciplines can implement automated verification or quality assessment will depend on the details of the field.