On linearity: straight lines, linear operators and the Fourier transform

abhipray.com

25 pointsbayeng3 comments

The article gives two definitions of linearity:

1) f(x) is linear if f(x)=(-a2/a1)x-b, and later

2) f(x) is linear if f(x1+x2)=f(x1)+f(x2)

But the function f(x)=x+1 is linear according to (1), but not according to (2). And there is no mention of affine functions, so it's not immediately clear why the same word is used to mean different things.

Good point, I'll patch it.

Thanks for a good article and actually very timely for me as I want to brush up on LA in 2019. From the above comment it sounds like you are the author? I’ve noted a few potential typos: 1) Length of v, should read length of a? 2) when discussing similarity between vectors you discuss the case of the dot product being 0 or 1, but the dot product could be >1, no?

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