To add to this: if you want an intermediate path that'll give a bit more insight than just basic linear algebra, reading a bit about Hilbert spaces might be worthwhile too. Depending which space(s) you choose to work in, it doesn't necessarily have to bog you down in coping with pathological cases. You probably will need to grok things like countability, limits and converge though.
The benefit: you get to pin down exactly what it means to talk about things like 'basis' and in particular 'orthogonal basis' in a meaningful way when it comes to infinite-dimensional spaces of functions like the ones the Fourier transform works on. Turns out you need some extra tools to do this; intuitions based only on experience with finite-dimensional linear algebra will likely have some handwavy gaps. (Not that that necessarily matters :)
About the article though: I really liked it. It wouldn't teach me from scratch how the transform works, but every extra bit of intuition one can get from looking at a concept from a different point of view helps, and this adds some extra physical intuition in a really nice way.
To add to this: if you want an intermediate path that'll give a bit more insight than just basic linear algebra, reading a bit about Hilbert spaces might be worthwhile too. Depending which space(s) you choose to work in, it doesn't necessarily have to bog you down in coping with pathological cases. You probably will need to grok things like countability, limits and converge though.
The benefit: you get to pin down exactly what it means to talk about things like 'basis' and in particular 'orthogonal basis' in a meaningful way when it comes to infinite-dimensional spaces of functions like the ones the Fourier transform works on. Turns out you need some extra tools to do this; intuitions based only on experience with finite-dimensional linear algebra will likely have some handwavy gaps. (Not that that necessarily matters :)
About the article though: I really liked it. It wouldn't teach me from scratch how the transform works, but every extra bit of intuition one can get from looking at a concept from a different point of view helps, and this adds some extra physical intuition in a really nice way.