Linear Algebra and Quantum Mechanics

When I was younger, I would occasionally hear about higher math classes that one was able to take. To me, then a naïve high schooler, AP Calculus represented an attainable pinnacle of mathematical knowledge beyond which lie a plethora of weird maths to explore. I had heard of multivariable calculus, which sounded like more of the same with more letters, differential equations, which was just calculus with more tricky problems, and so on and so forth.

However one, linear algebra, seemed like a mystery. It’s name evoked, to me, the kinds of problems done in middle school where I was painstakingly asked to grind through systems of three equations to find xy, and zSure, I thought, maybe there’s a use for solving ever bigger systems of equations of ever increasing complexity with bigger and better techniques. But, if multivariable and diff-E.Q. were “more of the same,” jumping back to middle school lines and planes was definitely going be a bore.

Spoiler alert: It wasn’t, and, while related, linear algebra really isn’t about that stuff. It’s actually about a lot of other, cooler stuff, including really cool stuff like quantum mechanics.

Note: This is just a primer on linear algebra. I introduce the axioms, and then paint over the subject with a broad brush that isn’t meant to be comprehensive. Quantum mechanics is inseparable from linear algebra, so I try to get to the meat of linear algebra while not glossing over too much. At the same time, this obviously shouldn’t be taken as a substitute for a more rigorous treatment of linear algebra.

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