Timeline for Norm bound of the entrywise logarithm of a stochastic matrix stationary matrix
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 10, 2012 at 21:12 | comment | added | Daniel86 | Sorry, it is indeed an irreducible Markov Chain. I edited. | |
| Nov 10, 2012 at 11:07 | history | edited | Daniel86 | CC BY-SA 3.0 |
added 33 characters in body
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| Nov 10, 2012 at 1:39 | comment | added | Steve Huntsman | @Suvrit: I would bet that $A$ is supposed to correspond to an irreducible Markov chain. | |
| Nov 9, 2012 at 23:33 | comment | added | Suvrit | For example, consider the identity matrix! | |
| Nov 9, 2012 at 23:32 | comment | added | Suvrit | Isn't it entirely possible that some entry of $A^p$ can be zero, in which case the lhs becomes unbounded, while the 2-norm of $A$ is well defined? | |
| Nov 9, 2012 at 23:02 | comment | added | Steve Huntsman | For $A$ sufficiently nice, its invariant distribution $p$ is given by $p = 1^*(I − A + 11^∗)^{−1}$, where here $1$ denotes a vector of ones. Moreover, $A^\infty = 1p$. Unfortunately, this is of precisely a form that will break if you try to use the Sherman-Morrison formula. | |
| Nov 9, 2012 at 21:11 | history | asked | Daniel86 | CC BY-SA 3.0 |