A new statement about the theorem determining the region of eigenvalues of stochastic matrices (Q1373321)
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scientific article; zbMATH DE number 1089499
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new statement about the theorem determining the region of eigenvalues of stochastic matrices |
scientific article; zbMATH DE number 1089499 |
Statements
A new statement about the theorem determining the region of eigenvalues of stochastic matrices (English)
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7 April 1998
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Let \(M_n\) denote the set of points in the complex plane that are eigenvalues of \(n\)-dimensional stochastic matrices. The set \(M_n\) is completely determined by a theorem of \textit{F. I. Karpelevich} [Izv. Akad. Nauk SSSR, Ser. Mat. 15, 361-383 (1951; Zbl 0043.01603)]. But his statement of the theorem is lengthy and the proof is too long and too involved. In this paper the author shortens the presentation of the theorem.
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stochastic matrix
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eigenvalues
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continued fractions
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Farey sequence
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