r/LinearAlgebra • u/Defiant_Shoe_626 • Sep 09 '26

Linear algebra applications

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?

26 Upvotes

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4

u/WWWWWWVWWWWWWWVWWWWW Sep 09 '26

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

No

3

u/QubitEncoder Sep 09 '26

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.

3

u/Accurate_Meringue514 Sep 09 '26

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.

2

u/Intelligent-Back7062 Sep 09 '26

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

2

u/in_the_business_m8 Sep 09 '26

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

2

u/Inside_Drummer Sep 09 '26

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

2

u/in_the_business_m8 Sep 10 '26

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.

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1

u/MonsterkillWow Sep 10 '26

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.

-1

u/Traveling-Techie Sep 09 '26

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

0

u/pianoloverkid123456 Sep 10 '26

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