Araştırma Makalesi
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On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers

Yıl 2023, Cilt: 27 Sayı: 5, 956 - 964, 18.10.2023
https://doi.org/10.16984/saufenbilder.1280572

Öz

-circulant matrices have applied in numerical computation, signal processing, coding theory, etc. In this study, our main goal is to investigate the r-circulant matrices of generalized Fermat numbers which are shown by We obtain the eigenvalues, determinants, sum identity of matrices. Also we find upper and lower bounds for the spectral norms of generalized Fermat r-circulant matrices. Beside these, we present 〖GR〗_(a,b,r)^* matrix in the form of the Hadamard product of two matrices as 〖GR〗_(a,b,r)^*=A.B. In addition, we get the right and skew-right circulant matrices for . Finally, we examine their different norms (Spectral and Euclidean) and limits for matrix norms.

Kaynakça

  • W. Weisstein, Eric, "Proth Number", mathworld.wolfram.com, 2019.
  • N. J. A. Sloane, “A Handbook of Integer Sequences”, Academic Press, New York, https://oeis.org, 1973.
  • Generalized Fermat numbers, OEIS. Generalized Fermat numbers - OeisWiki, 2022.
  • B. Fischer and J. Modersitzki, “Fast inversion of matrices arising in image processing”, Number Algorithms vol. 22 no.1, pp.1-11, 1999.
  • S. Georgiou and C. Kravvaritis, New good quasi-cyclic codes over GF(3), International Journal of Algebra vol.1, no.1, pp.11-24, 2007.
  • I. Kra and S. R. Simanca, On circulant matrices, Notices AMS vol.59, no.3, pp.368-377, 2012.
  • A. C. F. Bueno, “On the Eigenvalues and the Determinant of the Right Circulant Matrices with Pell and Pell–Lucas Numbers”, International Journal of Mathematics and Scientific Computing, vol.4, no.1, pp.19-20, 2014.
  • S. Solak, “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, vol.160, no.1, pp.125-132, 2005.
  • S. Shen, J. Cen, “On the bounds for the norms of r-circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, vol.216, no.10, pp. 2891-2897, 2010.
  • S. Q. Shen, J. M. Cen, “On the spectral norms of r-circulant matrices with the k-Fibonacci and k-Lucas numbers”, International Journal of Contemporary Mathematical Sciences,vol. 5, no. 12, pp. 569-578, 2010.
  • Y. Zheng, S. Shon, “Exact inverse matrices of Fermat and Mersenne circulant matrix”, In Abstract and Applied Analysis, Hindawi, 2015.
  • D. Bozkurt, T. Y. Tam, “Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal–Lucas numbers”, Applied Mathematics and Computation, vol.219, no. 2, pp.544-551, 2012.
  • M. Kumaria, K. Prasada, J. Tantib, and E. Özkan, “On the properties of г-circulant matrices involving Mersenne and Fermat numbers”, International Journal of Nonlinear Analysis and Applications, vol.1, no.11, 2023.
  • M. Marin, “Generalized solutions in elasticity of micropolar bodies with voids”, Revista de la Academia Canaria de Ciencias, vol.8, no.1, pp. 101-106, 1996
  • M. Marin, “Contributions on uniqueness in thermoelastodynamics on bodies with voids”, Ciencias matemáticas (Havana), vol.16, no.2, pp.101-109, 1998.
  • Z. Pucanovic, and M. Pesovic “Chebyshev polynomials and r-circulant matrices”, Applied Mathematics and Computation, vol.437, no.127521, 2023.
  • J. M. Blackledget, “Vector and Matrix norm”, Digital Signal Processing, pp.208-236, 2006.
  • Simon Foucart, http://www.math.drexel.edu/foucart/TeachingFiles/F12/M504Lect6.pdf
  • R. E. Cline, R. J. Plemmons, and G. Worm, “Generalized inverses of certain Toeplitz matrices”, Linear Algebra and its Application vol.8, no.1, pp.25-33, 1974.
  • K. Irwin, R. Santiago, Simanca, “On circulant matrices”, ://www.math.colombia.edu/ums/pdf/cir-not5.pdf
Yıl 2023, Cilt: 27 Sayı: 5, 956 - 964, 18.10.2023
https://doi.org/10.16984/saufenbilder.1280572

Öz

Kaynakça

  • W. Weisstein, Eric, "Proth Number", mathworld.wolfram.com, 2019.
  • N. J. A. Sloane, “A Handbook of Integer Sequences”, Academic Press, New York, https://oeis.org, 1973.
  • Generalized Fermat numbers, OEIS. Generalized Fermat numbers - OeisWiki, 2022.
  • B. Fischer and J. Modersitzki, “Fast inversion of matrices arising in image processing”, Number Algorithms vol. 22 no.1, pp.1-11, 1999.
  • S. Georgiou and C. Kravvaritis, New good quasi-cyclic codes over GF(3), International Journal of Algebra vol.1, no.1, pp.11-24, 2007.
  • I. Kra and S. R. Simanca, On circulant matrices, Notices AMS vol.59, no.3, pp.368-377, 2012.
  • A. C. F. Bueno, “On the Eigenvalues and the Determinant of the Right Circulant Matrices with Pell and Pell–Lucas Numbers”, International Journal of Mathematics and Scientific Computing, vol.4, no.1, pp.19-20, 2014.
  • S. Solak, “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, vol.160, no.1, pp.125-132, 2005.
  • S. Shen, J. Cen, “On the bounds for the norms of r-circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, vol.216, no.10, pp. 2891-2897, 2010.
  • S. Q. Shen, J. M. Cen, “On the spectral norms of r-circulant matrices with the k-Fibonacci and k-Lucas numbers”, International Journal of Contemporary Mathematical Sciences,vol. 5, no. 12, pp. 569-578, 2010.
  • Y. Zheng, S. Shon, “Exact inverse matrices of Fermat and Mersenne circulant matrix”, In Abstract and Applied Analysis, Hindawi, 2015.
  • D. Bozkurt, T. Y. Tam, “Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal–Lucas numbers”, Applied Mathematics and Computation, vol.219, no. 2, pp.544-551, 2012.
  • M. Kumaria, K. Prasada, J. Tantib, and E. Özkan, “On the properties of г-circulant matrices involving Mersenne and Fermat numbers”, International Journal of Nonlinear Analysis and Applications, vol.1, no.11, 2023.
  • M. Marin, “Generalized solutions in elasticity of micropolar bodies with voids”, Revista de la Academia Canaria de Ciencias, vol.8, no.1, pp. 101-106, 1996
  • M. Marin, “Contributions on uniqueness in thermoelastodynamics on bodies with voids”, Ciencias matemáticas (Havana), vol.16, no.2, pp.101-109, 1998.
  • Z. Pucanovic, and M. Pesovic “Chebyshev polynomials and r-circulant matrices”, Applied Mathematics and Computation, vol.437, no.127521, 2023.
  • J. M. Blackledget, “Vector and Matrix norm”, Digital Signal Processing, pp.208-236, 2006.
  • Simon Foucart, http://www.math.drexel.edu/foucart/TeachingFiles/F12/M504Lect6.pdf
  • R. E. Cline, R. J. Plemmons, and G. Worm, “Generalized inverses of certain Toeplitz matrices”, Linear Algebra and its Application vol.8, no.1, pp.25-33, 1974.
  • K. Irwin, R. Santiago, Simanca, “On circulant matrices”, ://www.math.colombia.edu/ums/pdf/cir-not5.pdf
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Bahar Kuloǧlu 0000-0001-7624-8270

Engin Eser 0000-0001-5965-4162

Engin Özkan 0000-0002-4188-7248

Erken Görünüm Tarihi 5 Ekim 2023
Yayımlanma Tarihi 18 Ekim 2023
Gönderilme Tarihi 10 Nisan 2023
Kabul Tarihi 13 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 27 Sayı: 5

Kaynak Göster

APA Kuloǧlu, B., Eser, E., & Özkan, E. (2023). On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers. Sakarya University Journal of Science, 27(5), 956-964. https://doi.org/10.16984/saufenbilder.1280572
AMA Kuloǧlu B, Eser E, Özkan E. On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers. SAUJS. Ekim 2023;27(5):956-964. doi:10.16984/saufenbilder.1280572
Chicago Kuloǧlu, Bahar, Engin Eser, ve Engin Özkan. “On the Properties of R-Circulant Matrices Involving Generalized Fermat Numbers”. Sakarya University Journal of Science 27, sy. 5 (Ekim 2023): 956-64. https://doi.org/10.16984/saufenbilder.1280572.
EndNote Kuloǧlu B, Eser E, Özkan E (01 Ekim 2023) On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers. Sakarya University Journal of Science 27 5 956–964.
IEEE B. Kuloǧlu, E. Eser, ve E. Özkan, “On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers”, SAUJS, c. 27, sy. 5, ss. 956–964, 2023, doi: 10.16984/saufenbilder.1280572.
ISNAD Kuloǧlu, Bahar vd. “On the Properties of R-Circulant Matrices Involving Generalized Fermat Numbers”. Sakarya University Journal of Science 27/5 (Ekim 2023), 956-964. https://doi.org/10.16984/saufenbilder.1280572.
JAMA Kuloǧlu B, Eser E, Özkan E. On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers. SAUJS. 2023;27:956–964.
MLA Kuloǧlu, Bahar vd. “On the Properties of R-Circulant Matrices Involving Generalized Fermat Numbers”. Sakarya University Journal of Science, c. 27, sy. 5, 2023, ss. 956-64, doi:10.16984/saufenbilder.1280572.
Vancouver Kuloǧlu B, Eser E, Özkan E. On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers. SAUJS. 2023;27(5):956-64.

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