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Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri

Year 2022, , 148 - 154, 28.12.2022
https://doi.org/10.46810/tdfd.994281

Abstract

Bu çalışmada n pozitif tamsayı olmak üzere herhangi negatif determinantlı nxn boyutlu çift devirli matrislerin özdeğerlerinin yerlerini belirleyen sonuçlar ortaya konulmuştur. Bu sonuçlar ortaya konulurken özdeğerlerin matris elemanlarının sürekli fonksiyonu oluşu kullanılmıştır.

References

  • [1] Amster P, Idels L. New applications of M matrix methods to stability of high-order linear delayed equations. Appl. Math. Lett. 2016;54:1-6.
  • [2] Bendito E, Carmona A, Encinas AM, Mitjana M. The M matrix ınverse problem for singular and symmetric Jacobi matrices. Linear Algebra Appl. 2012;436:1090-1098.
  • [3] Brandts J, Cihangir A. Geometric aspects of the symmetric ınverse M matrix problem. Linear Algebra Appl. 2016;506:33-81.
  • [4] Baker CE, Mityagin BS. Location of eigenvalues of doubly cyclic matrices. Linear Algebra Appl. 2018;540:160-202.
  • [5] Chandrashekaran A, Parthasarathy T, Ravindran G. On strong Z matrices. Linear Algebra Appl. 2010;432:964-969.
  • [6] Guan J. Modified alternately linearized ımplicit ıteration method for M matrix algebraic Riccati equations. Appl. Math. Comput. 2019;347:442-448.
  • [7] Horn RA, Johnson CR. Topics in matrix analysis. Cambridge, Cambridge University Press; 1991.
  • [8] Hershkowitz D, Schneider H. On the generalized nullspace of M matrices and Z matrices. Linear Algebra Appl. 1988;106:5-23.
  • [9] Hershkowitz D, Schneider H. Solution of Z matrix equations. Linear Algebra Appl. 1988;106:25-38.
  • [10] Jeffries CD, Johnson CR, Zhou T, Simpson DA, Kaufmann WK. A flexible and qualitatively stable model for cell cycle dynamics ıncluding dna damage effect. Gene Regulation and Systems Biology. 2012;1:55-66.
  • [11] Johnson CR, Price Z, Spitkovsky IM. The distribution of eigenvalues of doubly cyclic Z^+ matrices. Linear Algebra Appl. 2013;439:3576-3580.
  • [12] Kalman D, White JE. Polynomial equation and circulant matrices. Amer. Math. Monthly. 2001;108(9):821-840.
  • [13] Lu L, Ahmed Z, Guan J. Numerical methods for a quadratic matrix equation with a nonsingular M matrix. Appl.Math.Lett. 2016;52:46-52.
  • [14] Li C, Zhang F. Eigenvalue continuity and Gersgorin’s Theorem. Electron. J. Linear Algebra. 2019;35:619-625.

Location of Eigenvalues of Doubly Cyclic Z^+ Matrices

Year 2022, , 148 - 154, 28.12.2022
https://doi.org/10.46810/tdfd.994281

Abstract

In this study, the results that determine locations of the eigenvalues of any nxn doubly cyclic Z^+ matrices with negative determinant are presented. While establishing these results, the fact that any eigenvalue of a matrix is a continuous function of entries of the matrix is used.

References

  • [1] Amster P, Idels L. New applications of M matrix methods to stability of high-order linear delayed equations. Appl. Math. Lett. 2016;54:1-6.
  • [2] Bendito E, Carmona A, Encinas AM, Mitjana M. The M matrix ınverse problem for singular and symmetric Jacobi matrices. Linear Algebra Appl. 2012;436:1090-1098.
  • [3] Brandts J, Cihangir A. Geometric aspects of the symmetric ınverse M matrix problem. Linear Algebra Appl. 2016;506:33-81.
  • [4] Baker CE, Mityagin BS. Location of eigenvalues of doubly cyclic matrices. Linear Algebra Appl. 2018;540:160-202.
  • [5] Chandrashekaran A, Parthasarathy T, Ravindran G. On strong Z matrices. Linear Algebra Appl. 2010;432:964-969.
  • [6] Guan J. Modified alternately linearized ımplicit ıteration method for M matrix algebraic Riccati equations. Appl. Math. Comput. 2019;347:442-448.
  • [7] Horn RA, Johnson CR. Topics in matrix analysis. Cambridge, Cambridge University Press; 1991.
  • [8] Hershkowitz D, Schneider H. On the generalized nullspace of M matrices and Z matrices. Linear Algebra Appl. 1988;106:5-23.
  • [9] Hershkowitz D, Schneider H. Solution of Z matrix equations. Linear Algebra Appl. 1988;106:25-38.
  • [10] Jeffries CD, Johnson CR, Zhou T, Simpson DA, Kaufmann WK. A flexible and qualitatively stable model for cell cycle dynamics ıncluding dna damage effect. Gene Regulation and Systems Biology. 2012;1:55-66.
  • [11] Johnson CR, Price Z, Spitkovsky IM. The distribution of eigenvalues of doubly cyclic Z^+ matrices. Linear Algebra Appl. 2013;439:3576-3580.
  • [12] Kalman D, White JE. Polynomial equation and circulant matrices. Amer. Math. Monthly. 2001;108(9):821-840.
  • [13] Lu L, Ahmed Z, Guan J. Numerical methods for a quadratic matrix equation with a nonsingular M matrix. Appl.Math.Lett. 2016;52:46-52.
  • [14] Li C, Zhang F. Eigenvalue continuity and Gersgorin’s Theorem. Electron. J. Linear Algebra. 2019;35:619-625.
There are 14 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Murat Sarduvan 0000-0001-7049-8922

Hande Neziroğlu 0000-0003-1948-3068

Publication Date December 28, 2022
Published in Issue Year 2022

Cite

APA Sarduvan, M., & Neziroğlu, H. (2022). Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri. Türk Doğa Ve Fen Dergisi, 11(4), 148-154. https://doi.org/10.46810/tdfd.994281
AMA Sarduvan M, Neziroğlu H. Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri. TDFD. December 2022;11(4):148-154. doi:10.46810/tdfd.994281
Chicago Sarduvan, Murat, and Hande Neziroğlu. “Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri”. Türk Doğa Ve Fen Dergisi 11, no. 4 (December 2022): 148-54. https://doi.org/10.46810/tdfd.994281.
EndNote Sarduvan M, Neziroğlu H (December 1, 2022) Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri. Türk Doğa ve Fen Dergisi 11 4 148–154.
IEEE M. Sarduvan and H. Neziroğlu, “Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri”, TDFD, vol. 11, no. 4, pp. 148–154, 2022, doi: 10.46810/tdfd.994281.
ISNAD Sarduvan, Murat - Neziroğlu, Hande. “Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri”. Türk Doğa ve Fen Dergisi 11/4 (December 2022), 148-154. https://doi.org/10.46810/tdfd.994281.
JAMA Sarduvan M, Neziroğlu H. Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri. TDFD. 2022;11:148–154.
MLA Sarduvan, Murat and Hande Neziroğlu. “Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri”. Türk Doğa Ve Fen Dergisi, vol. 11, no. 4, 2022, pp. 148-54, doi:10.46810/tdfd.994281.
Vancouver Sarduvan M, Neziroğlu H. Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri. TDFD. 2022;11(4):148-54.