The non-negative matrix A is mixing means there exists an m, such that every entries of A^m is positive.
If the matrix after removing is still mixing, the problem will be solved by Perron-Frobenius theorem. If not, I don't how to solve it.
Asked
Active
Viewed 32 times
0
-
Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Dec 21 '24 at 07:50
-
https://math.stackexchange.com/a/924257 – user1551 Dec 21 '24 at 08:52
-
you can take $A$ to have spectral radius of $1$ and it is similar to an irreducible markov matrix via a positive diagonal matrix, then apply https://math.stackexchange.com/questions/4888565/markov-chain-transition-matrix-eigenvalues-textbook-exercise/ . I suggest "proof 2" where you don't need to consider the (ir)reducibility of the dominated matrix. – user8675309 Dec 21 '24 at 18:18