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    The Karpelevic region revisited

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    Karpelevic_JMAA_revision.pdf (672.7Kb)
    Date
    2020
    Author
    Kirkland, S.
    Laffey, T.
    Smigoc, H.
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    Abstract
    We consider the Karpelevic region \Theta_n in the complex plane consisting of all eigenvalues of all stochastic matrices of order n. We provide an alternative characterisation of \Theta_n that sharpens the original description given by Karpelevic. In particular, for each \theta in [0; 2\pi); we identify the point on the boundary of \Theta_n with argument \theta. We further prove that if n is a natural number with n at least 2, and t is in \Theta_n, then t is a subdominant eigenvalue of some stochastic matrix of order n.
    URI
    http://hdl.handle.net/1993/34813
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