On controllability of the real shifted inverse power iteration

Controllability properties of the inverse power method on projective space are investigated. For complex eigenvalue shifts a simple characterization o f the reachable sets in terms of invariant subspaces can be obtained. The r eal case is more complicated and is investigated in this paper. Necessary a nd sufficient conditions for complete controllability are obtained in terms of the solvability of a matrix equation. Partial results on conditions for the solvability of this matrix equation are given. (C) 2001 Elsevier Scien ce B.V. All rights reserved.