Heh. Well my definition of "basics" is probably different from most peoples. That's actually not too ridiculous. The topics are closely related and form a pretty common 1-1.5 semester class for physical science majors. You want a book like this one. Stick to the first 3 units of the book and you'll be ok.
And in answer to your actual question: eigenvalues, eigenvalues, eigenvalues. By far the core idea at the intersection of those three topics.
Computational neuroscience--I don't have details beyond that unfortunately, just what the instructor said in response to my question about what math I should know.
Aha! That's very helpful. Check out Anderson's "Introduction to Neural Networks" textbook, the one with the white and purple cover. It develops exactly the parts of linear algebra, multivariable, and differential equations that you need in order to do neural network stuff. It's also very readable. You'll be able to skim the biology, and all of the math will be motivated by the applications you're interested in. Most school libraries should have a copy.
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And in answer to your actual question: eigenvalues, eigenvalues, eigenvalues. By far the core idea at the intersection of those three topics.
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