Geodesic
Eigenvalue distribution of certain ray patterns
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 749-762.

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In this paper, the eigenvalue distribution of complex matrices with certain ray patterns is investigated. Cyclically real ray patterns and ray patterns that are signature similar to real sign patterns are characterized, and their eigenvalue distribution is discussed. Among other results, the following classes of ray patterns are characterized: ray patterns that require eigenvalues along a fixed line in the complex plane, ray patterns that require eigenvalues symmetric about a fixed line, and ray patterns that require eigenvalues to be in a half-plane. Finally, some generalizations and open questions related to eigenvalue distribution are mentioned.
Classification : 15A18, 15A57
Keywords: eigenvalue distribution; ray patterns; sign patterns; sector patterns; cyclically real; signature similarity; cycles 
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     author = {Eschenbach, Carolyn A. and Hall, Frank J. and Li, Zhongshan},
     title = {Eigenvalue distribution of certain ray patterns},
     journal = {Czechoslovak Mathematical Journal},
     pages = {749--762},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2000},
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     zbl = {1079.15504},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000__50_4_a5/}
}
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Eschenbach, Carolyn A.; Hall, Frank J.; Li, Zhongshan. Eigenvalue distribution of certain ray patterns. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 749-762. http://geodesic.mathdoc.fr/item/CMJ_2000__50_4_a5/