On the combinatorial identities using the nth power of square matrix
*Gopal K. GohelCorresponding authorgopalgohel.maths@ddu.ac.inDepartment of MathematicsDharmsinh Desai UniversityNadiad, Gujarat, IndiaView full profile → , Kailash M. Patilkailashpatil2111.maths@ddu.ac.inDepartment of MathematicsDharmsinh Desai UniversityNadiad, Gujarat, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Published Online:
- 19 Mar 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1808
- Pages:
- 181–189
Abstract
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References
[1] Rakesh Barai and Anuradha S Garge. Trace and discriminate criteria for a matrix to be a sum of sixth and eighth powers of matrices. arXiv preprint arXiv:2012.13855, (2020).
[2] Claude Brezinski, Paraskevi Fika, and Marilena Mitrouli. Estimations of the trace of power of positive self-adjoint operators by extrapolation of the moments. ElectronTrans. Numer. Anal., 39 : 144–155, (2012).
[3] Saber N. Elaydi and William A. Harris Jr. On the Computation of An. Siam Review, 40(4) : 965–971, (1998).
[4] Dinesh J. Karia, Kailash M. Patil, and H.P. Singh. On the sum of powers of square matrices. Oper. Matrices, 13(1) : 221–229, (2019).
[5] M. Kwapisz. Remarks on the calculation of the power of a matrix. Journal of Difference Equations and Applications, 10(2) : 139–149, (2004).
[6] James Mc Laughlin and B. Sury. Powers of a matrix and combinatorial identities. Integers: Electronic J. Combinatorial Number Theory, A13, 5 : 1–9, (2005).
[7] Sarah Lee, David Chen, and Jennifer Zhang. Efficient computation of the matrix exponential using the nth power of a matrix. Linear Algebra and its Applications, 25(4) : 789–804, (2022).
[8] Chao Ma, Qimiao Xie, and Jin Zhong. Matrices whose powers eventually have certain properties. Oper Matrices, 13 : 323–331, (2019).
[9] Marvin Marcus and Morris Newman. The sum of the elements of the powers of a matrix.Pacific J. Math., 12 : 627–635, (1962).
[10] James Mc Laughlin. Combinatorial identities deriving from the nth power of a 2× 2 matrix. Integers, 4 : A19, (2004).
[11] K.M. Patil. On the trace of powers of square matrices. Hacet. J. Math. Stat., 50(1) : 14–23.(2021).
[12] B Sury. A curious polynomial identity. Nieuw Arch. Wisk.(4), 11(2) : 93–96, (1993).
[13] Annamalai, N. & Durairajan, C. Codes from the incidence matrices of a Zero-divisor graphs, Journal of Discrete Mathematical Sciences and Cryptography, 26 : 2, 377-385,(2023).
[14] Al-Dolat, Mohammed & Al-Zoubi, Khaldoun, General upper bounds for the numerical radius on complex Hilbert space, Journal of Interdisciplinary Mathematics, 26 : 4, 761–774, (2023).
[15] A. Abu-Omar, F. Kittaneh, Numerical radius inequalities for n×n operator matrices. Linear Algebra Appl. 468, 18–26. (2015).




