Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri

Year 2022, Volume: 11 Issue: 4, 148 - 154, 28.12.2022

Murat Sarduvan , Hande Neziroğlu

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.

Keywords

Çift devirli matris, özdeğerlerin yerleri, bir polinomun sıfırları

Location of Eigenvalues of Doubly Cyclic Z^+ Matrices

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.

Keywords

Doubly cyclic - matrix, Eigenvalue location, Zeros of a polinomial

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.