> The discrete fourier transform is actually finite-dimensional linear algebra.
Not only that, it's the most interesting kind of linear algebra: it shows that, though every (finite-dimensional if you don't like choice) vector space has a basis—so that we can pretend that all n-dimensional vector spaces are the same for a fixed n—the simple act of changing that basis (which is all the DFT is doing) can have a profound impact.
Not only that, it's the most interesting kind of linear algebra: it shows that, though every (finite-dimensional if you don't like choice) vector space has a basis—so that we can pretend that all n-dimensional vector spaces are the same for a fixed n—the simple act of changing that basis (which is all the DFT is doing) can have a profound impact.