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No, it opens up a whole new suite of questions. Now we can ask, for example: what conditions do we need for the result to hold? What dimensions does it hold in? And many more...

Interesting; can you provide some references for this way of thinking?

I read their previous post, and nowhere do they explicitly say "a transform is a...". One might assume that it is indeed a linear transformation, as you suggest, but it shouldn't b…

What is meant by a Transform in this context? The author doesn't seem to give a definition.

Out of interest, what sort of company/industry do you work in where you're able to work on this kind of thing?