I'm new to this website and I hope my question isn't too weird. So, I have to diagonalize numerically an integral operator. Integral means, an operator that takes the input function $f(x)$ and returns the function $ g(x) = \int K(x,y) f(y)$. If I'm not mistaken $K(x,y)$ is called the "kernel" of this operator.
If $x$ is a single real variable, I know how to do this. I consider discrete points along the x-line, and the values taken by $K(x,y)$ on the resulting grid form a matrix! This matrix (call it $M$) can be diagonalized using any math software. Like, by writing eig(M) in MATLAB. But what if $x$ is a vector, which is a set of two or three variables?
How would you proceed in that case? Even if I discretize the variables, $K(x,y)$ doesn't become a matrix but something more weird, a tensor. I can't use MATLAB's eig function on that. Then what can I do? A huge thanks if you can help.