How Can Markov Models Be Used to Compare Transition State Matrices?

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Markov models can effectively compare transition state matrices, but challenges arise due to the zero element in the 4x4 matrices. Averaging the diagonal elements is insufficient as it discards valuable data from the other matrix elements. The determinant is also not a viable option due to its sensitivity to single value changes. Eigenvalues and eigenvectors are suggested as a more reliable method for comparison, particularly when there are no absorbing states. Utilizing these mathematical concepts can provide a clearer understanding of the similarities between the transition state matrices.
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I have a problem where I get 3 or 4x4 matrices and I'd like to compare them. The matrices are transition states so markov models are applicable, but I can't find anything about how to compare the matrices for similarity. One solution that has been done is to agv the diagonal, but since the 4,4 element is always zero, your only using 3 numbers of the 16 and throwing the rest away. The determinant has no correlation between the system so can't be used since it is too affected by single value changes. Does anyone know of another method I might be able to use?
Steve Brailsford
 
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I would use eigenvalues. If the processes don't have any absorbing states then the eigenvectors corresponding to eigenvector 1 is the stationary state.
 

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