he was a physics and math major and did not know eigenvectors and eigenvalues? i would like to know how is this possible. can someone explain it to me?
He is a bit older. Linear algebra is also very old, but it didn't really become the field we know today until the 1950s. I would add that in 2025 it is cheap to buy a computer that can solve large linear systems, but that certainly wasn't true in 1975, so linear algebra was less applicable in the real world.
I am not too familiar with the pedagogical history of linear algebra, but I've been reading some advanced undergraduate geometry texts from the 30s-60s and linear algebra was generally not an assumed prerequisite. There was a particular separation between the studies of "two and three dimensional vector spaces over R" (largely geometric) versus "finite dimensional vector spaces over a field" (entirely algebraic), and determinants were presented directly as volume computations. These days undergraduates mostly treat R^2 and R^3 algebraically, maybe at the expense of geometric understanding. (E.g. Euler's rotation theorem is easily proved when restated as a theorem about matrices over R^3 with determinant +1, but Euler's original statement and proof using spherical trigonometry is deeper.)
I was a double major, one in physics, in the 80s. After the three semester engineering physics classes, intro QM was taught spring sophomore year. We used Liboff. In addition, it was required for all physics, chem and engineering majors to take math 20(5?) which was linear algebra.
And given that most of basic QM was formalized by 1930 and relies upon eigenvectors, hard to see any physics course taught since that time not having it.
Whoa, Liboff, that book... I only vaguely remember it now (took QM in 1988). I took "math for mathematicians" (Math 25) instead of "math for physicists" (Math 22?), but remember my classmates who took first year "math for physicists" got eigenvectors very quickly right off the bat in the pre-published book they used https://www.cambridge.org/core/books/course-in-mathematics-f...
I was introduced to eigenvectors in a math course on linear algebra. They seemed esoteric but I could prove theorems and stuff… cool but kind of forgettable.
Then I took quantum mechanics. That’s where I learned eigensystems. That’s where their utility and beauty were beaten into me, problem set by problem set. In quantum mechanics, eigensystems are ubiquitous: from using ladder operators to solve the harmonic oscillator in an elegant way, to what quantum numbers actually are, to the reason behind the Heisenberg uncertainty principle, and to the so many different ways to use perturbation theory to explain atomic and molecular spectra.
You can do the basics of quantum mechanics without explicit linear algebra, and many intro physical chemistry texts aren’t able to assume the math as a pre-requisite and have to do that. But it’s tedious and awkward, like trying to learn physics without calculus.
Same boat as the author here, except I switched from physics to software after year three.
I had never heard of them until I was _years_ into software engineering. I think this is more common than you may think. I had never dealt with linear algebra in a formal setting, despite leveraging a lot of the concepts, until then.
I asked myself the same thing. The article said “learn” Linear Algebra, not “review” Linear Algebra. Do some undergrad math programs not teach Linear Algebra?
In my experience (maths degrees at two universities with >15000 students, one of which I now teach at) group theory and abstract algebra more generally are much more likely to be part of a maths degree than topology. I've never heard anyone describe topology that way.
Speaking as a CS/Math dual major from the late 1980s, the explanations in the textbook were ... uselessly bad where I went (SFU). So while I know the math involved, I didn't know the terms until I retook it from a teacher who actually taught worth anything, years later.
(I still don't use the terms, they're not very ... well, they're awkward and while my embedded work sometimes calls for the math, the terms ... meh. There are clearer ways to put things!).
I am not too familiar with the pedagogical history of linear algebra, but I've been reading some advanced undergraduate geometry texts from the 30s-60s and linear algebra was generally not an assumed prerequisite. There was a particular separation between the studies of "two and three dimensional vector spaces over R" (largely geometric) versus "finite dimensional vector spaces over a field" (entirely algebraic), and determinants were presented directly as volume computations. These days undergraduates mostly treat R^2 and R^3 algebraically, maybe at the expense of geometric understanding. (E.g. Euler's rotation theorem is easily proved when restated as a theorem about matrices over R^3 with determinant +1, but Euler's original statement and proof using spherical trigonometry is deeper.)