I am trying to find the equation I would need to use in order to implement a Least Squares Kernel classifier for a dataset with $N$ samples of feature length $d$. I have the kernel equation $k(x_i, x_j)$ and I need the equation to plug it into to get the length-d vector used to classify future data. No matter where I look/google, Although there are dozens of powerpoints and pdfs that seem to give me almost what I'm looking for, I can't find a resource which can give me a straight answer.
Note: I am not looking for the programming-language tool that computes this for me such as lsqlin, but the mathematical formula, or series of formulae.