Difference between Ritz vectors and Eigenvectors This is probably a silly question, as it came from an error in the Eigenvectors I found using ARPACK (Fortran). In this case, the values of the Ritz vectors are identical in value to the theoretical Eigenvectors but different in sign. So what is the real difference between the two? Should I expect this behavior?

First of all, the eigenvectors corresponding to eigenvalues of multiplicity one are only unique up to a scalar. Hence, if $v$ is an eigenvector, so is $\mu v$ for $\mu \in \mathbb{C}$.
Let me turn to the definition of Ritz vectors. Ritz vectors are usually approximations to the eigenvectors of a matrix $A$ that are obtained using the Arnoldi method (see here). The Arnoldi method computes a matrix $H_m$ and $V_m$. If $y$ is an eigenvectors of the matrix $H_m$, then $V_m y$ is called the Ritz vectors and approximate the eigenvectors of $A$.
More generally, if $q_1, \dots, q_m$ is a set of normalized and orthogonal vectors and $Q_m = [ q_1 | \dots | q_m ]$. Then if $y$ is an eigenvector of $Q_m^T A Q_m$, then $Q_m y$ is called a Ritz vector and the corresponding eigenvalue a Ritz value of $A$ w.r.t. the subspace $\mathrm{span}\{q_1, \dots, q_m\}$.
In the case of the Arnoldi method, we have $Q_m = V_m$ and $H_m = Q_m^T A Q_m$.
