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Is abstract linear algebra required for a deep understanding of statistics? I'm a computer science major deciding between a linear algebra for applications class versus a very theoretical proof based linear algebra class (where they don't cover applied linear algebra).

I'm very interested in the field of statistics and would like a deep understanding of how the statistical tools are developed and used. That being said I'm not very keen on mathematical proofs and would rather not take this class if I don't have to.

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I think an applied linear algebra class is perfect, since doing statistics you will probably use finite vectors space over the real numbers field.

If someday you need a more specific background in other vector spaces, it won't be hard to expand some concepts and theorems. If it is usefull to statistics that you learn finite vector spaces, you will see it in the applied linear algebra course and learn why it's important.

There is no problem in doing an abstract course, but having constant contact with applications is really good. In my case, I did an abstract course and later, an applied extension course. The first one was really helpfull to understand concepts, but the second one was the most significant to my projects (mainly because it had some programming activities with linear algebra too).

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