TY - JOUR T1 - Çift Devirli Z^+-Matrislerin Özdeğerlerinin Yerleri TT - Location of Eigenvalues of Doubly Cyclic Z^+ Matrices AU - Sarduvan, Murat AU - Neziroğlu, Hande PY - 2022 DA - December DO - 10.46810/tdfd.994281 JF - Türk Doğa ve Fen Dergisi JO - TJNS PB - Bingol University WT - DergiPark SN - 2149-6366 SP - 148 EP - 154 VL - 11 IS - 4 LA - tr AB - 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. KW - Çift devirli matris KW - özdeğerlerin yerleri KW - bir polinomun sıfırları N2 - 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. CR - [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. CR - [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. CR - [3] Brandts J, Cihangir A. Geometric aspects of the symmetric ınverse M matrix problem. Linear Algebra Appl. 2016;506:33-81. CR - [4] Baker CE, Mityagin BS. Location of eigenvalues of doubly cyclic matrices. Linear Algebra Appl. 2018;540:160-202. CR - [5] Chandrashekaran A, Parthasarathy T, Ravindran G. On strong Z matrices. Linear Algebra Appl. 2010;432:964-969. CR - [6] Guan J. Modified alternately linearized ımplicit ıteration method for M matrix algebraic Riccati equations. Appl. Math. Comput. 2019;347:442-448. CR - [7] Horn RA, Johnson CR. Topics in matrix analysis. Cambridge, Cambridge University Press; 1991. CR - [8] Hershkowitz D, Schneider H. On the generalized nullspace of M matrices and Z matrices. Linear Algebra Appl. 1988;106:5-23. CR - [9] Hershkowitz D, Schneider H. Solution of Z matrix equations. Linear Algebra Appl. 1988;106:25-38. CR - [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. CR - [11] Johnson CR, Price Z, Spitkovsky IM. The distribution of eigenvalues of doubly cyclic Z^+ matrices. Linear Algebra Appl. 2013;439:3576-3580. CR - [12] Kalman D, White JE. Polynomial equation and circulant matrices. Amer. Math. Monthly. 2001;108(9):821-840. CR - [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. CR - [14] Li C, Zhang F. Eigenvalue continuity and Gersgorin’s Theorem. Electron. J. Linear Algebra. 2019;35:619-625. UR - https://doi.org/10.46810/tdfd.994281 L1 - https://dergipark.org.tr/en/download/article-file/1969900 ER -