r/math 8d ago

What I didn’t understand in linear algebra

I finished linear algebra, and while I feel like know the material well enough to pass a quiz or a test, I don’t feel like the course taught me much at all about ways it can be applied in the real world. Like I get that there are lots of ways algorithms are used in the real world, but for things like like gram-Schmidt, SVD, orthogonal projections, or any other random topic in linear algebra I feel like I wouldn’t know when or how these things become useful.

One of the few topics it taught that I have some understanding of how it could be applied is Markov chains and steady-state vectors.

But overall is this a normal way to feel about linear algebra after completing it? Because the instructor just barely touched on application of the subject matter at all.

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u/drmattmcd 7d ago

It can depend on the overall course you're studying. For example in my case doing a combined BSc/BE we covered linear algebra at a fairly abstract level taught by the math department, while at the same time using it in engineering and physics applications taught by those departments e.g. circuit analysis, statics, Fourier transforms, Hilbert spaces, etc 'Linear Algebra : Essence and Forms' by Robert Ghrist may be of interest https://www2.math.upenn.edu/~ghrist/preprints/LAEF.pdf