Approximate matrix with k-largest eigenvalues

Using Scipy's sparse.linalg.eigs package, one can find the $$k$$-largest eigenvalues and corresponding eigenvectors (each of size $$n$$) of an $$n \times n$$ matrix. I was wondering if it would be possible to use these eigenvalues/vectors to approximate the original matrix. For a full eigenvalue decomposition, one could do $$A = V \Lambda V^{-1}$$, where $$V$$ is the matrix of eigenvalues and $$\Lambda$$ is the diagonal matrix of eigenvalues. But since for the partial decomposition $$V$$ is of size $$n \times k$$, it is invertible. Still, is there any way to reconstruct $$A$$ from the largest eigenvalues/vectors?

(not sure if this helps, but in my case $$A$$ is Hermitian and relatively sparse)