I worry that this tweet will be wildly unpopular, I do, but I must press on: Does anyone out there have a plain-English, intuitive definition of "linear transformation"?
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The same broad approach can be taken with addition. There it's very context-dependent - hopefully you have a context where some vector-like object is in the picture, and can be used to construct examples of what linearity means, and of what it does not.
I've never ended up using these explanations. But I've occasionally pondered putting them into something introductory. In general, with abstract things like this I like the trick of explaining examples which violate the definition. It seems to help readers a lot, at least IME.
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I'll be curious to see what you come up with! I've really enjoyed many of your articles; it's fun to explain how I'd respond to this challenge. Hope it was at least a tiny bit helpful!
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Very helpful, thank you! Y'all are so smart. I should have asked hours ago.
End of conversation
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