"d = eigs(Afun,n,___) specifies a function handle Afun instead of a matrix. The second input n gives the size of matrix A used in Afun. You can optionally specify B, k, sigma, opts, or name-value pairs as additional input arguments."
The "Eigenvalues Using Function Handle" example on that page shows the general technique. While that example actually constructs and factors the A matrix, creating the matrix explicitly is not necessary. eigs doesn't care whether you do or even can explicitly create the matrix A inside your function so long as your Afun function computes some function of A and a vector x (usually either A*x or A\x depending on the value you specify for sigma.) See the documentation for the Afun input argument on that page for more information about how it interacts with sigma.
