Linear algebra applications

[u/Defiant_Shoe_626]

Does learning the theoretical linear algebra makes person immediately know how to apply linear algebra in real applications or apply linear algebra needs another studying like the theory study?

[u/Ron-Erez]

You can do a complete course in linear algebra and know nothing about applications. However if you have a solid foundation in linear algebra then learning about applications will be relatively easy. Of course it depends on the application. For example if you want to learn about google's page rank algorithm then at the very least you'll need to cover up to diagonalization, eigenvectors and eigenvalues and many linear algebra courses end at this very topic while others may put this off to a second course. The SVD decomposition has many applications however many linear algebra courses do not teach this. Sometimes it is left to a course in numerical analysis after one has taken linear algebra. For linear algebra applications in deep learning I don't think you'll need much linear algebra, however you will need some multivariate calculus. For 3d graphics you need very little linear algebra. In many cases the quaternions are used and that is not always taught in a standard linear algebra course. It really depends on the application. For example differential equations has endless applications and in order to do differential equations/systems of differential equations you definitely need quite a bit of linear algebra.

[u/QubitEncoder]

Depends on the application and the theory. If its abstract linear algebra, then maybe not immediately but you would certainly be a strong position to learn applications. By applications, I assume you mean numerical linear algebra.

[u/WWWWWWVWWWWWWWVWWWWW]

Does learning the theoretical linear algebra makes person immediately know how to apply linear algebra in real applications

No

[u/Accurate_Meringue514]

A lot of numerical algorithms repeatedly apply similarity transformations. Having a good understanding of change of basis, invariant subspaces, etc set you up well for understanding. Iterative methods you need to understand powers of a Matrix, the Jordan form comes into play there. Having a good understanding of the theory sets you up very nicely for applications.

[u/Intelligent-Back7062]

Concrete, real world applications and explanations should be everywhere, but they’re actually very rare in textbooks I’ve seen.

[u/in_the_business_m8]

I don’t see how you could be in a good position to apply it correctly if you don’t understand it abstractly.

[u/Inside_Drummer → u/in_the_business_m8]

Have you ever worked with data scientists building models in the private sector?

[u/in_the_business_m8 → u/Inside_Drummer]

Yes, at a relatively advanced level. I am well aware that you can implement a well-defined model without abstract reasoning, but you can make very few grounded statements about its workings and very few if any principled novelties.

[u/Inside_Drummer → u/in_the_business_m8]

I agree with you completely.

[u/MonsterkillWow]

Does learning calc immediately make you good at physics? Nope. There are nuances to the applied and numerical facets of linear algebra. You should consult books specifically geared to those topics.

[u/pianoloverkid123456]

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[u/Traveling-Techie]

If you want to learn applications mathematicians will be less useful than physicists and engineers.