The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
For an m-state homogeneous Markov chain whose one-step transition matrix is T, the group inverse, A#, of the matrix A = 1 - T is shown to play a central role. For an ergodic chain, it is demonstrated that virtually everything that one would want to known about the chain can be determined by computin...
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| Veröffentlicht in: | SIAM review 1975-07, Vol.17 (3), p.443-464 |
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| container_title | SIAM review |
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| creator | Meyer, Carl D. |
| description | For an m-state homogeneous Markov chain whose one-step transition matrix is T, the group inverse, A#, of the matrix A = 1 - T is shown to play a central role. For an ergodic chain, it is demonstrated that virtually everything that one would want to known about the chain can be determined by computing A#. Furthermore, it is shown that the introduction of A#into the theory of ergodic chains provides not only a theoretical advantage, but it also provides a definite computational advantage that is not realized in the traditional framework of the theory. |
| doi_str_mv | 10.1137/1017044 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0036-1445 |
| ispartof | SIAM review, 1975-07, Vol.17 (3), p.443-464 |
| issn | 0036-1445 1095-7200 |
| language | eng |
| recordid | cdi_proquest_journals_926192809 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; LOCUS - SIAM's Online Journal Archive |
| subjects | Algebra Eigenvalues Ergodic theory Jordan matrices Logical proofs Markov analysis Markov chains Mathematical vectors Matrices Matrix inversion |
| title | The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains |
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