I'm not sure, if I fully understand your question. I doubt however, that there is a straightforward method for calculating the eigenvector corresponding to the largest eigenvalue of the covariance matrix without calculating all eigenvalues first (at least not for non-sparse matrices).
If you want the first principal component of the (m x n)-matrix A containing m measurements as row vectors you would in general do the following:
A = randn(100, 20);
c_A = cov(A);
[V, ~], eigs( c_A );
p_1 = V( :, 1 );
which gives you the direction of the first principal component in the variable p_1.