Is there a setting in which finding eigenvalues/eigenvectors is computationally hard? Or at least, not known to be computationally easy?For example, how computationally hard or easy is it to find eigenvalues/eigenvectors of matrices over finite fields?  Suppose the field has size exponential in the dimension.  (Does the QR algorithm still converge?)How about finding eigenvalues/eigenvectors of sparse matrices? 
Hardness of finding eigenvalues?
linear algebra