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Year 2019, Volume: 48 Issue: 3, 689 - 699, 15.06.2019
https://doi.org/10.15672/hujms.552204

Abstract

References

  • M. Andrecut, Applications of left circulant matrices in signal and image processing, Modern Physics Letters B 22, 231–241, 2008.
  • W. Bani-Domi and F. Kittaneh, Norm equalities and inequalities for operator matrices, Linear Algebra Appl. 429, 57–67, 2008.
  • D. Bozkurt and T.Y. Tam, Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas numbers, Appl. Math. Comput. 219, 544–551, 2012.
  • A. Cambini, An explicit form of the inverse of a particular circulant matrix, Discrete Math. 48, 323–325, 1984.
  • M. Elia, Derived sequences, the Tribonacci recurrence and cubic forms, Fibonacci Quart. 39, 107–115, 2001.
  • A.E. Gilmour, Circulant matrix methods for the numerical solution of partial differential equations by FFT convolutions, Appl. Math. Model. 12, 44–50, 1988.
  • I.J. Good, On the inversion of circulant matrices, Biometrika 37, 185–186, 1950.
  • X.Y. Jiang and K.C. Hong, Exact determinants of some special circulant matrices involving four kinds of famous numbers, Abstr. Appl. Anal. Article ID 273680, 12 pages, 2014.
  • X.Y. Jiang and K.C. Hong, Explicit inverse matrices of Tribonacci skew circulant type matrices, Appl. Math. Comput. 268, 93–102, 2015.
  • Z.L. Jiang, Y.P. Gong and Y. Gao, Circulant type matrices with the sum and product of Fibonacci and Lucas numbers, Abstr. Appl. Anal. Article ID 375251, 12 pages, 2014.
  • Z.L. Jiang, Y.P. Gong and Y. Gao, Invertibility and explicit inverses of circulanttype matrices with k-Fibonacci and k-Lucas numbers, Abstr. Appl. Anal. Article ID 238953, 10 pages, 2014.
  • X.Q. Jin, V.K. Sin and L.L. Song, Circulant-block preconditioners for solving ordinary differential equations, Appl. Math. Comput. 140, 409–418, 2003.
  • Y. Jing and H. Jafarkhani, Distributed differential space-time coding for wireless relay networks, IEEE Transactions on Communications 56, 1092–1100, 2008.
  • H. Karner, J. Schneid, and C.W. Ueberhuber, Spectral decomposition of real circulant matrices, Linear Algebra Appl. 367, 301–311, 2003.
  • F. Liao, Q. Wang, and M. Niu, Property and application of one class of generalized Tribonacci sequence, Pure Mathematics(Chinese) 1, 15–20, 2011.
  • L. Liu and Z. Jiang, Explicit form of the inverse matrices of Tribonacci circulant type matrices, Abstr. Appl. Anal. Article ID 169726, 10 pages, 2015.
  • T. Mansour and M. Shattuck, Polynomials whose coefficients are generalized Tribonacci numbers, Appl. Math. Comput. 219, 8366–8374, 2013.
  • S.Q. Shen, J.M. Cen and Y. Hao, On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput. 217, 9790–9797, 2011.
  • G.Q. Wang and S.S. Cheng, 6-periodic travelling waves in an artificial neural network with bang-bang control, J. Differ. Equa. Appl. 18, 261–304, 2012.
  • Y. Yazlik and N. Taskara, On the inverse of circulant matrix via generalized k- Horadam numbers, Appl. Math. Comput. 223, 191–196, 2013.
  • Y. Zheng and S. Shon, Exact determinants and inverses of generalized Lucas skew circulant type matrices, Appl. Math. Comput. 270, 105–113, 2015.

Explicit inverses of generalized Tribonacci circulant type matrices

Year 2019, Volume: 48 Issue: 3, 689 - 699, 15.06.2019
https://doi.org/10.15672/hujms.552204

Abstract

In this paper, we consider generalized Tribonacci circulant type matrices, including the circulant and left circulant. Firstly, we discuss the invertibility of generalized Tribonacci circulant matrix and give the explicit determinant and inverse matrix based on constructing the transformation matrices. Afterwards, by utilizing the relation between circulant and left circulant, the invertibility of generalized Tribonacci left circulant matrix is also discussed. The determinant and inverse of generalized Tribonacci left circulant matrix are given respectively.

References

  • M. Andrecut, Applications of left circulant matrices in signal and image processing, Modern Physics Letters B 22, 231–241, 2008.
  • W. Bani-Domi and F. Kittaneh, Norm equalities and inequalities for operator matrices, Linear Algebra Appl. 429, 57–67, 2008.
  • D. Bozkurt and T.Y. Tam, Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas numbers, Appl. Math. Comput. 219, 544–551, 2012.
  • A. Cambini, An explicit form of the inverse of a particular circulant matrix, Discrete Math. 48, 323–325, 1984.
  • M. Elia, Derived sequences, the Tribonacci recurrence and cubic forms, Fibonacci Quart. 39, 107–115, 2001.
  • A.E. Gilmour, Circulant matrix methods for the numerical solution of partial differential equations by FFT convolutions, Appl. Math. Model. 12, 44–50, 1988.
  • I.J. Good, On the inversion of circulant matrices, Biometrika 37, 185–186, 1950.
  • X.Y. Jiang and K.C. Hong, Exact determinants of some special circulant matrices involving four kinds of famous numbers, Abstr. Appl. Anal. Article ID 273680, 12 pages, 2014.
  • X.Y. Jiang and K.C. Hong, Explicit inverse matrices of Tribonacci skew circulant type matrices, Appl. Math. Comput. 268, 93–102, 2015.
  • Z.L. Jiang, Y.P. Gong and Y. Gao, Circulant type matrices with the sum and product of Fibonacci and Lucas numbers, Abstr. Appl. Anal. Article ID 375251, 12 pages, 2014.
  • Z.L. Jiang, Y.P. Gong and Y. Gao, Invertibility and explicit inverses of circulanttype matrices with k-Fibonacci and k-Lucas numbers, Abstr. Appl. Anal. Article ID 238953, 10 pages, 2014.
  • X.Q. Jin, V.K. Sin and L.L. Song, Circulant-block preconditioners for solving ordinary differential equations, Appl. Math. Comput. 140, 409–418, 2003.
  • Y. Jing and H. Jafarkhani, Distributed differential space-time coding for wireless relay networks, IEEE Transactions on Communications 56, 1092–1100, 2008.
  • H. Karner, J. Schneid, and C.W. Ueberhuber, Spectral decomposition of real circulant matrices, Linear Algebra Appl. 367, 301–311, 2003.
  • F. Liao, Q. Wang, and M. Niu, Property and application of one class of generalized Tribonacci sequence, Pure Mathematics(Chinese) 1, 15–20, 2011.
  • L. Liu and Z. Jiang, Explicit form of the inverse matrices of Tribonacci circulant type matrices, Abstr. Appl. Anal. Article ID 169726, 10 pages, 2015.
  • T. Mansour and M. Shattuck, Polynomials whose coefficients are generalized Tribonacci numbers, Appl. Math. Comput. 219, 8366–8374, 2013.
  • S.Q. Shen, J.M. Cen and Y. Hao, On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput. 217, 9790–9797, 2011.
  • G.Q. Wang and S.S. Cheng, 6-periodic travelling waves in an artificial neural network with bang-bang control, J. Differ. Equa. Appl. 18, 261–304, 2012.
  • Y. Yazlik and N. Taskara, On the inverse of circulant matrix via generalized k- Horadam numbers, Appl. Math. Comput. 223, 191–196, 2013.
  • Y. Zheng and S. Shon, Exact determinants and inverses of generalized Lucas skew circulant type matrices, Appl. Math. Comput. 270, 105–113, 2015.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Shouqiang Shen This is me 0000-0003-0504-3344

Weijun Liu This is me 0000-0003-2396-637X

Lihua Feng This is me 0000-0003-4144-1649

Publication Date June 15, 2019
Published in Issue Year 2019 Volume: 48 Issue: 3

Cite

APA Shen, S., Liu, W., & Feng, L. (2019). Explicit inverses of generalized Tribonacci circulant type matrices. Hacettepe Journal of Mathematics and Statistics, 48(3), 689-699. https://doi.org/10.15672/hujms.552204
AMA Shen S, Liu W, Feng L. Explicit inverses of generalized Tribonacci circulant type matrices. Hacettepe Journal of Mathematics and Statistics. June 2019;48(3):689-699. doi:10.15672/hujms.552204
Chicago Shen, Shouqiang, Weijun Liu, and Lihua Feng. “Explicit Inverses of Generalized Tribonacci Circulant Type Matrices”. Hacettepe Journal of Mathematics and Statistics 48, no. 3 (June 2019): 689-99. https://doi.org/10.15672/hujms.552204.
EndNote Shen S, Liu W, Feng L (June 1, 2019) Explicit inverses of generalized Tribonacci circulant type matrices. Hacettepe Journal of Mathematics and Statistics 48 3 689–699.
IEEE S. Shen, W. Liu, and L. Feng, “Explicit inverses of generalized Tribonacci circulant type matrices”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, pp. 689–699, 2019, doi: 10.15672/hujms.552204.
ISNAD Shen, Shouqiang et al. “Explicit Inverses of Generalized Tribonacci Circulant Type Matrices”. Hacettepe Journal of Mathematics and Statistics 48/3 (June 2019), 689-699. https://doi.org/10.15672/hujms.552204.
JAMA Shen S, Liu W, Feng L. Explicit inverses of generalized Tribonacci circulant type matrices. Hacettepe Journal of Mathematics and Statistics. 2019;48:689–699.
MLA Shen, Shouqiang et al. “Explicit Inverses of Generalized Tribonacci Circulant Type Matrices”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, 2019, pp. 689-9, doi:10.15672/hujms.552204.
Vancouver Shen S, Liu W, Feng L. Explicit inverses of generalized Tribonacci circulant type matrices. Hacettepe Journal of Mathematics and Statistics. 2019;48(3):689-9.