I'm using an iterative subspace algorithm (dsrrit) to obtain the eigenvalues of an eigenvector equation $$ -\nabla^2 \mathbf{x} = \lambda\mathbf{x} $$ where $\nabla^2$ is the usual Laplacian operator. The algorithm returns a set of eigenvalues $\lambda$ and a subspace $Q$ that spans the eigenvectors of $\lambda$.
The literature states
"the programs do not produce a set of eigenvectors corresponding to the eigenvalues computed" ... "If explicit eigenvectors are desired, they may be obtained by evaluating the eigenvectors of $T$ and applying (2)."
but I have plotted the vectors in the returned subspace $Q$ and they do indeed match the expected eigenvectors of $\lambda$. Are there particular conditions that guarantee this? (My eigenvectors are real, and my operator is represented by a symmetric matrix)