> 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.
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.