Çift Devirli  Z^+-Matrislerin Özdeğerlerinin Yerleri
                                    
                                 
                                
                                    
                                                                                                                                                                                                                        Year 2022,
                                                                                        Volume: 11 Issue: 4,                                                                                                                 148 - 154,                                     28.12.2022                                
                                
                                                                                                                        
                                                                                                                                                
                                                        Murat Sarduvan
                                                                                                                    
                                                                                                            
                                                
                                                                                                    ,
                                                
                                                                                                                                
                                                                                                                                                
                                                        Hande Neziroğlu
                                                                                                            
                                                
                                                
                                                                                                                                                                                            
                                                                    
                                
                                
                                                                    
                                        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,
                                                                                        Volume: 11 Issue: 4,                                                                                                                 148 - 154,                                     28.12.2022                                
                                
                                                                                                                        
                                                                                                                                                
                                                        Murat Sarduvan
                                                                                                                    
                                                                                                            
                                                
                                                                                                    ,
                                                
                                                                                                                                
                                                                                                                                                
                                                        Hande Neziroğlu
                                                                                                            
                                                
                                                
                                                                                                                                                                                            
                                                                    
                                
                                
                                                                    
                                        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.