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Proceedings of the American Mathematical Society

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Concerning diagonal similarity of irreducible matrices


Author: D. J. Hartfiel
Journal: Proc. Amer. Math. Soc. 30 (1971), 419-425
MSC: Primary 15.60
DOI: https://doi.org/10.1090/S0002-9939-1971-0281731-5
MathSciNet review: 0281731
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Abstract: If $ A = ({a_{ij}})$ is an $ n \times n$ irreducible matrix, then there are positive numbers $ {d_1},{d_2}, \cdots $, $ {d_n}$ so that $ \sum\nolimits_k {{d_i}{a_{ik}}d_k^{ - 1} = } \sum\nolimits_k {{d_k}{a_{ki}}d_i^{ - 1}} $ for each $ i \in \{ 1,2, \cdots ,n\} $. Further, the numbers $ {d_1},{d_2}, \cdots $, $ {d_n}$ are unique up to scalar multiples.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0281731-5
Keywords: Irreducible, diagonally similar, matrix patterns
Article copyright: © Copyright 1971 American Mathematical Society