My version was: the course boils down to just two things: anything that is linear behaves like matrix multiplication; eigenvectors are the ones that don’t change direction.
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The problem is that the teachers themselves often do not have this "factored" perspective.
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Yes… that became my suspicion in retrospect… MIT math professors didn’t really understand the subjects they were teaching.
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You say this, but if you actually try to write a book that, say, proves these facts or uses them in a useful way, you quickly find yourself piling up a heap of facts you forgot were needed to get to "the four." I know because I'm currently waist-deep in the pile.
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That’s interesting! I haven’t taught it, so My intuition may be way off
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