That face when you realize Integral Transforms are just the matrix multiplication formula between a matrix and a column vector for infinite dimensional Hilbert space!

Now what about Matrix-Matrix multiplication in Hilbert space? 8>

And then *Matrix inversion*!!? 8D

Which, would be a way of producing the inverse kernel of an arbitrary integral transform, right? :D

(That is, a roadmap of how to find a closed-form solution and/or a numerical approximation technique :> )

(Although numerical approximation is inherently finite-dimensional, so perhaps normal linear algebra, itself, serves as the numerical approximation of inverting integral transforms :> )

Puppy Pi@codepuppy@mathstodon.xyzNow what about Matrix-Matrix multiplication in Hilbert space? 8>

And then *Matrix inversion*!!? 8D

Which, would be a way of producing the inverse kernel of an arbitrary integral transform, right? :D

(That is, a roadmap of how to find a closed-form solution and/or a numerical approximation technique :> )

(Although numerical approximation is inherently finite-dimensional, so perhaps normal linear algebra, itself, serves as the numerical approximation of inverting integral transforms :> )