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Sep 18, 2016 at 15:29 comment added Ludwig It's a long story, but basically I would like to show that the iteration $(\star)$ has no invariant trajectories in the set of positive definite trace one matrices if $A\neq I$
Sep 18, 2016 at 15:20 comment added Nawaf Bou-Rabee Could you please elaborate? What is the motivation for this question?
Sep 18, 2016 at 15:19 comment added Ludwig Unfortunately, yes
Sep 18, 2016 at 15:18 comment added Nawaf Bou-Rabee Does the restriction that $A$ has the same eigenvectors as $X_0$ reduce the practicality of this result?
Sep 18, 2016 at 13:56 comment added Ludwig Thanks! The approach is interesting, although restricted to a particular case.
Sep 17, 2016 at 18:04 history edited Nawaf Bou-Rabee CC BY-SA 3.0
I added more detail to clarify the problem this answer addresses.
Sep 17, 2016 at 16:22 history edited Nawaf Bou-Rabee CC BY-SA 3.0
deleted 152 characters in body
Sep 17, 2016 at 15:33 history answered Nawaf Bou-Rabee CC BY-SA 3.0