[aje403]

This is frightening but believable. I've worked with a few "quants" who stared at me doe eyed explaining eigen* and basic calculus concepts to them in the context of why their calculations don't add up. You mention you've used fourier transforms before - if you don't understand an eigenbasis then you don't have a fundamental understanding the math you're deploying.

[ajross]

> You mention you've used fourier transforms before - if you don't understand an eigenbasis then you don't have a fundamental understanding the math you're deploying.

That's a bit uncharitable. A fourier decomposition can absolutely be understood as an explicit bag of calculus tricks, with no loss of precision or generality. And an awful lot can be done with just those tools -- you don't need to explain JPEG compression or VLBI astronomy in terms of eigenvectors, for example.

Obviously (heh, "obviously") it's true that the space of decomposed functions form an orthogonal basis, so technically we're "really" operating in a linear space and that has expressive power too. But there are lots of ways of looking at problems.

To wit, you're not wrong. You're just... Well, you know.

[aje403]

Dude your post is orthogonal

[xevb3k]

In the context I used it, FFT wasn’t really of fundamental importance. Using FFT (and in particular FFTW) gave a performance improvement (execution speed), but no real advantage in terms of accuracy over an alternative naive method...

So... yes I guess I’ve just not seen anywhere in my work where this stuff has proved useful...

[aje403]

It's pretty much ubiquitous in any quantitative field... would not even know where to start