Certainly you would want a more abstract follow up for many cases. Even engineering or computer science students may have to learn about e.g. inner product spaces and orthogonal polynomials for their numerics class.

Obligatory remark that "reading" a math textbook, and even moreso a basic one, is an active task; you can get the intuitions from youtube videos of the 3Blue1Brown variety, but to really learn you need to follow the text closely, put question marks on passages you're not 120% comfortable with, do the proofs that are left to the reader and the recommended exercises. If you're super comfortable with the material, you should do the more challenging exercises, usually marked with asterisks.

Basically you need a pencil, a lot of scratch paper and a capable waste basket; or a whiteboard all to yourself (but I get tired from being on my feet for hours on end).

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E: My litmus test is the Gershgorin circle theorem. Every so often I check if I can still prove it, and if I do I try to review the surrounding matrix. I will literally vote against hiring anyone who can't at least handwave why that's true.

>My litmus test is the Gershgorin circle theorem. Every so often I check if I can still prove it, and if I do I try to review the surrounding matrix. I will literally vote against hiring anyone who can't at least handwave why that's true.

Interesting comment with no context—i.e. not hire someone for what? I don't know if I would ever not hire someone for not understanding a math problem (unless the job was heavily math related in the sphere of the problem). I would definitely not hire someone who communicates as ineffectively as you did in this comment.

Reminds me of: http://philip.greenspun.com/humor/mcdonalds-joke

Purely out of curiosity, what jobs is your employer trying to fill that an intuitive understanding of said theorem is required?

I took a lot of linear algebra and I can’t recall having covered it.

> I will literally vote against hiring anyone who can't at least handwave why that's true.

I hope you're at least hiring for a machine learning engineer and not a general software engineer to build CRUD apps.