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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And it seems that the kind/degree of understanding required to write a textbook with a novel structuring of the material is greater still. (I’m attempting this now…)
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The hardest part probably is the structure. When I think about linear algebra, I have a family of densely interconnected concepts to play with; but when I teach I have to explain one thing at a time. So I can't explain how I really think about it until the last week of class.
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