Inverse elementary divisors problem for doubly stochastic matrices^†

This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-79-0127

Abstract

Question:Given a doubly stochastic matrix A, do there exist doubly stochastic matrices with the same spectrum as A but with arbitrarily prescribed elementary divisors that do not include (λ−1) ^k with k > 1? The question is answered in the negative in general, and in the affirmative if A is a diagonalizable doubly stochastic matrix with positive entries and real eigenvalues, and also if A is a doubly stochastic n × nmatrix with n−1 equal eigenvalues.

This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-79-0127

This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-79-0127

Notes

This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-79-0127