# Creating a matrix from a function

Consider a function $$f(a, b)$$, where $$0 leq a, b leq k$$, and $$a$$ and $$b$$ are integers, for some known $$k$$.

I am looking for a short and efficient code to put these values into a matrix, such that the code can handle large values of $$k$$. That is, I am looking for a code that creates the $$k times k$$ matrix:

$$begin{equation} F = begin{pmatrix} f(1, 1)~~~f(1, 2) ~~~~~ cdots ~~~~~~~ f(1, k) \ f(2, 1)~~~f(2, 2) ~~~~~ cdots ~~~~~~~ f(2, k) \ cdots \ f(k, 1)~~~f(k, 2) ~~~~~ cdots ~~~~~~~ f(k, k) end{pmatrix}. end{equation}$$

I could only define the matrix by hand for a few small values of $$k$$.