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Local nonlinear optimizations can be found locally by constructing linear approximations of the problem statement near the initial conditions, so that is actually connected with Linear Algebra. The issue here is that most students spend only a short time of their life getting exposed to fundamental topics like linear algebra, that's not the time to waste their attention on hype of the month

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But most of these students (particularly ones taking the lin alg course that apparently has APPLIED in all caps in the title) are going to be engineers or similar who will never encounter the fundamentals outside of their application in tools like k means. Teaching them an abstract field without connections to what motivates it (intellectually or practically) is pedagogically not ideal.

>Teaching them an abstract field without connections to what motivates it (intellectually or practically) is pedagogically not ideal.

While fair in general, the point is k means has nothing to do with linear algebra besides they both use numbers sometimes. It would be like sandwiching in a chapter on RSA crypto because it's interesting and number-y but still has no connection to linear algebra.

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