Eigenvalue distribution of certain ray patterns

Carolyn A. Eschenbach; Frank J. Hall; Zhongshan Li

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 4, page 749-762
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Eschenbach, Carolyn A., Hall, Frank J., and Li, Zhongshan. "Eigenvalue distribution of certain ray patterns." Czechoslovak Mathematical Journal 50.4 (2000): 749-762. <http://eudml.org/doc/30598>.

@article{Eschenbach2000,
abstract = {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.},
author = {Eschenbach, Carolyn A., Hall, Frank J., Li, Zhongshan},
journal = {Czechoslovak Mathematical Journal},
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},
language = {eng},
number = {4},
pages = {749-762},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Eigenvalue distribution of certain ray patterns},
url = {http://eudml.org/doc/30598},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Eschenbach, Carolyn A.
AU - Hall, Frank J.
AU - Li, Zhongshan
TI - Eigenvalue distribution of certain ray patterns
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 4
SP - 749
EP - 762
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/30598
ER -

References

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  3. 10.1017/S0004972700031518, Bull. Austral. Math. Soc. 57 (1998), 159–172. (1998) MR1623848DOI10.1017/S0004972700031518
  4. 10.1080/03081089108818079, Linear and Multilinear Algebra 29 (1991), 299–311. (1991) MR1119461DOI10.1080/03081089108818079
  5. Sign patterns that require repeated eigenvalues, Linear Algebra Appl. 190 (1993), 169–179. (1993) MR1230357
  6. The Feynman Lectures on Physics, vol. III, Addison-Wesley, 1965. (1965) MR0213079
  7. On the period and base of a sign pattern matrix, Linear Algebra Appl. 212/213 (1994), 101–120. (1994) MR1306974
  8. Ray patterns of matrices and nonsingularity, Linear Algebra Appl. 267 (1997), 359–373. (1997) MR1479127
  9. 10.1137/0617062, SIAM J. Matrix Anal. Appl. 17 (1996), 1020–1024. (1996) MR1410715DOI10.1137/0617062

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