I have been thinking about the following problem, and haven't been able to get anywhere.
Given a block matrix $X=[X_1,...,X_p]$ where $X_{n\times k}$ and $X_{i_{n\times k_i}}$. Assuming we know that all the eigenvalues of $X_i'X_i$ are below one, ¿is it possible to deduce something regarding the eigenvalues of $X'X$?