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Keywords:
eigenvalue distribution; ray patterns; sign patterns; sector patterns; cyclically real; signature similarity; cycles
eigenvalue distribution; ray patterns; sign patterns; sector patterns; cyclically real; signature similarity; cycles
Summary:
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.
References:
[1] C. A. Eschenbach: Sign patterns that require exactly one real eigenvalue. Linear and Multilinear Algebra 35 (1993), 213–224. DOI 10.1080/03081089308818259 | MR 1308691 | Zbl 0787.15008
[2] C. A. Eschenbach, F. J. Hall and Z. Li: Eigenvalue frequency and consistent sign pattern matrices. Czechoslovak Math. J. 44(119) (1994), 461–479. MR 1288165
[3] C. A. Eschenbach, F. J. Hall and Z. Li: From real to complex sign pattern matrices. Bull. Austral. Math. Soc. 57 (1998), 159–172. DOI 10.1017/S0004972700031518 | MR 1623848
[4] C. A. Eschenbach and C. R. Johnson: Sign patterns that require real, nonreal or pure imaginary eigenvalues. Linear and Multilinear Algebra 29 (1991), 299–311. DOI 10.1080/03081089108818079 | MR 1119461
[5] C. A. Eschenbach and C. R. Johnson: Sign patterns that require repeated eigenvalues. Linear Algebra Appl. 190 (1993), 169–179. MR 1230357
[6] R. Feynman, R. Leighton and M. Sands: The Feynman Lectures on Physics, vol. III. Addison-Wesley, 1965. MR 0213079
[7] Z. Li, F. J. Hall and C. A. Eschenbach: On the period and base of a sign pattern matrix. Linear Algebra Appl. 212/213 (1994), 101–120. MR 1306974
[8] J. McDonald, D. Olesky, M. Tsatsomeros and P. van den Driessche: Ray patterns of matrices and nonsingularity. Linear Algebra Appl. 267 (1997), 359–373. MR 1479127
[9] J. Rohn and G. Rex: Interval P-matrices. SIAM J. Matrix Anal. Appl. 17 (1996), 1020–1024. DOI 10.1137/0617062 | MR 1410715
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