1
vote
2answers
24 views

Transition Matrix eigenvalues constaints

I have a Transition Matrix, i.e. a matrix whose items are bounded between 0 and 1 and either rows or columns sum to one. I would like to know if it is possible that in any such matrices the ...
0
votes
1answer
15 views

How many iterations are generally required when using the power iteration method?

Suppose I have an n x n matrix and I want to find the dominant eigenvalue and its associated eigenvector. Given these dimensions, what is the minimum number of iterations of the power iteration ...
0
votes
0answers
16 views

Random Walk Prediction on a grid using markov chain

We have a m*n Grid and n no of robots in that grid which would perform a random walk simultaneously.Each robot can move in 4 direction specifically Up, Left, Down, Right. After x steps the random ...
2
votes
1answer
75 views

Proof that Markov Chains converges to the stationary distribution

Let $P$ is a transition matrix of a Markov Chain, which is irreducible, aperiodic and lets assume $\pi$ is its stationary distribution: $\pi = \pi P$. Does anyone knows the proof for the following ...
1
vote
1answer
83 views

Markov Chain Solution Eigenvalue

I am having trouble understanding how to solve for the state vector at time $t$ for a markov chain using matrix algebra. I have the following Markov Transition Intensity Matrix, for the states A, N, ...
1
vote
1answer
90 views

Steady State Markov Chain

I was reading http://www.ams.org/bookstore/pspdf/mbk-58-prev.pdf and going through the first example for the frog jumping between the lily pads. I'm interested in find the steady-state probability for ...
1
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1answer
182 views

Eigenvector of transition matrix for Markov chain

Why is the only eigenvector of the transition matrix for an irreducible Markov chain with eigenvalue $= 1$ the eigenvector with all ones?
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votes
1answer
70 views

Bounding the smallest eigenvalue of an ergodic Markov Chain

I am trying to prove that the smallest eigenvalue of an ergodic Markov chain is greater than -1. Can we do that using proof by contradiction, i.e. assuming the smallest eigenvalue being -1, etc.? The ...
13
votes
1answer
400 views

Eigenvalues for $3\times 3$ stochastic matrices

This is a plot of the non-real eigenvalues of 10000 randomly generated $3\times3$ stochastic matrices. It's pretty clear that they lie in the convex hull of the three cube roots of unity. The ...
2
votes
1answer
335 views

Eigenvalues of a infinitesimal generator matrix

Consider a Markov process on a finite state space $S$, whose dynamic is determined by a certain infinitesimal generator $Q$ (that is a matrix in this case) and an initial distribution $m$. 1) Is ...
0
votes
2answers
1k views

What is the eigenvalue of stochastic matrix?

I have a stochastic matrix $A \in R^{n \times n}$ whose sum of the entries in each row is 1. When I found out the eigenvalues and eigenvectors for this stochastic matrix, it always happens that one of ...