Skip to main content

Determinant of the Generalized Lucas RSFMLR Circulant Matrices in Communication

  • Conference paper
Information Computing and Applications (ICICA 2013)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 391))

Included in the following conference series:

  • 1555 Accesses

Abstract

In this paper, the explicit determinants are presented by using generalized Lucas numbers. The techniques used herein are based on the inverse factorization of polynomial. Firstly, we introduce the definitions of the RSFMLR and RSLMFL circulant matrices in communication, and properties of the related generalized Lucas numbers. Then, we present the main results and the detailed process.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Michele, E.: Derived Sequences, the Tribonacci Recurrence and Cubic Forms. Fibonacci Quart. 39(2), 107–115 (2001)

    MathSciNet  MATH  Google Scholar 

  2. Davis, P.: Circulant Matrices. Wiley, New York (1979)

    MATH  Google Scholar 

  3. David, C.: Regular Representations of Semisimple Algebras, Separable Field Extensions, Group Characters, Generalized Circulants, and Generalized Cyclic Codes. Linear Algebra and its Appl. 218, 147–183 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jaiswal, D.: On Determinants Involving Generalized Fibonacci Numbers. Fibonacci Quart. 7, 319–330 (1969)

    MathSciNet  MATH  Google Scholar 

  5. Lin, D.: Fibonacci-Lucas Quasi-cyclic Matrices. Fibonacci Quart. 40, 280–286 (2002)

    MathSciNet  MATH  Google Scholar 

  6. Lind, D.: A Fibonacci Circulant. Fibonacci Quart. 8, 449–455 (1970)

    MathSciNet  MATH  Google Scholar 

  7. Shen, S.Q., Cen, J.M., Hao, Y.: On the Determinants and Inverses of Circulant Matrices with Fibonacci and Lucas Numbers. Appl. Math. Comput. 217, 9790–9797 (2011)

    MathSciNet  MATH  Google Scholar 

  8. Akbulak, M., Bozkurt, D.: On the Norms of Toeplitz Matrices Involving Fibonacci and Lucas Numbers. Hacet. J. Math. Stat. 37, 89–95 (2008)

    MathSciNet  MATH  Google Scholar 

  9. Lee, G.Y., Kim, J.S., Lee, S.G.: Factorizations and Eigenvalues of Fibonacci and Symmetric Fibonacci Matrices. Fibonacci Quart. 40, 203–211 (2002)

    MathSciNet  MATH  Google Scholar 

  10. Miladinović, M., Stanimirović, P.: Singular Case of Generalized Fibonacci and Lucas Matrices. J. Korean Math. Soc. 48, 33–48 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Stanimirović, P., Nikolov, J., Stanimirović, I.: A generalization of Fibonacci and Lucas matrices. Discrete Appl. Math. 156, 2606–2619 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jiang, X.Y., Gao, Y., Jiang, Z.L.: Explicit Determinants and Inverses of Skew Circulant and Skew Left Circulant Matrices Involving the k-Fibonacci Numbers in Communications-I. Far East Journal of Mathematical Sciences 76(1), 123–137 (2013)

    MATH  Google Scholar 

  13. Jiang, Z.L., Zhou, Z.X.: Circulant Matrices. Chengdu Technology University Publishing Company, Chengdu (1999)

    Google Scholar 

  14. Jiang, X.Y., Jiang, Z.L.: Efficient Algorithm for Finding Inverse and Group Inverse of the RSFPrLR Circulant Matrix in Codes. JP Journal of Algebra, Number Theory and Applications 29(1), 51–70 (2013)

    MathSciNet  MATH  Google Scholar 

  15. Tian, Z.P.: Fast Algorithms for Solving the Inverse Problem of Ax=b in the Class of the ULS r-circulant (retrocirculant) Matrices. Int. J. Algebra 5, 9403–9411 (2011)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zheng, Y., Shon, S., Lee, S., Oh, D. (2013). Determinant of the Generalized Lucas RSFMLR Circulant Matrices in Communication. In: Yang, Y., Ma, M., Liu, B. (eds) Information Computing and Applications. ICICA 2013. Communications in Computer and Information Science, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53932-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-53932-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53931-2

  • Online ISBN: 978-3-642-53932-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics