Year 2020, Volume 12 , Issue 2, Pages 76 - 85 2020-12-31

On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers

Mustafa BAHŞİ [1] , Süleyman SOLAK [2]


In this paper, we compute the spectral norms of $r-$ circulant matrices with the hyper-Fibonacci and hyper-Lucas numbers of the forms $F_{r}=Circ-r(F_k^{(0)},F_k^{(1)},...,F_k^{(n-1)}) $$L_r=Circ-r(L_{k}^{\left( 0\right) },L_{k}^{\left( 1\right) },...,L_{k}^{\left( n-1\right) })$ and their Hadamard and Kronecker products. For this, we firstly compute the spectral and Euclidean norms of circulant matrices of the forms $F=Circ(F_{k}^{\left( 0\right) }, F_{k}^{\left( 1\right) },... ,F_{k}^{\left( n-1\right) })$ and $L=Circ(L_{k}^{\left( 0\right) },L_{k}^{\left( 1\right) },...,L_{k}^{\left( n-1\right) })$. Moreover, we give some examples related to special cases of our results.

Circulant matrix, r-circulant matrix, hyper- Fibonacci numbers, hyper-Lucas numbers, Euclidean norm, spectral norm
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Primary Language en
Subjects Mathematics
Journal Section Articles
Authors

Orcid: 0000-0002-6356-6592
Author: Mustafa BAHŞİ (Primary Author)
Institution: AKSARAY UNIVERSITY
Country: Turkey


Orcid: 0000-0003-4085-277X
Author: Süleyman SOLAK
Institution: Necmettin Erbakan University
Country: Turkey


Dates

Publication Date : December 31, 2020

Bibtex @research article { tjmcs715052, journal = {Turkish Journal of Mathematics and Computer Science}, issn = {}, eissn = {2148-1830}, address = {}, publisher = {Matematikçiler Derneği}, year = {2020}, volume = {12}, pages = {76 - 85}, doi = {10.47000/tjmcs.715052}, title = {On The Norms of Another Form of \$r-\$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers}, key = {cite}, author = {Bahşi, Mustafa and Solak, Süleyman} }
APA Bahşi, M , Solak, S . (2020). On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers . Turkish Journal of Mathematics and Computer Science , 12 (2) , 76-85 . DOI: 10.47000/tjmcs.715052
MLA Bahşi, M , Solak, S . "On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers" . Turkish Journal of Mathematics and Computer Science 12 (2020 ): 76-85 <https://dergipark.org.tr/en/pub/tjmcs/issue/58180/715052>
Chicago Bahşi, M , Solak, S . "On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers". Turkish Journal of Mathematics and Computer Science 12 (2020 ): 76-85
RIS TY - JOUR T1 - On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers AU - Mustafa Bahşi , Süleyman Solak Y1 - 2020 PY - 2020 N1 - doi: 10.47000/tjmcs.715052 DO - 10.47000/tjmcs.715052 T2 - Turkish Journal of Mathematics and Computer Science JF - Journal JO - JOR SP - 76 EP - 85 VL - 12 IS - 2 SN - -2148-1830 M3 - doi: 10.47000/tjmcs.715052 UR - https://doi.org/10.47000/tjmcs.715052 Y2 - 2020 ER -
EndNote %0 Turkish Journal of Mathematics and Computer Science On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers %A Mustafa Bahşi , Süleyman Solak %T On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers %D 2020 %J Turkish Journal of Mathematics and Computer Science %P -2148-1830 %V 12 %N 2 %R doi: 10.47000/tjmcs.715052 %U 10.47000/tjmcs.715052
ISNAD Bahşi, Mustafa , Solak, Süleyman . "On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers". Turkish Journal of Mathematics and Computer Science 12 / 2 (December 2020): 76-85 . https://doi.org/10.47000/tjmcs.715052
AMA Bahşi M , Solak S . On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers. TJMCS. 2020; 12(2): 76-85.
Vancouver Bahşi M , Solak S . On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers. Turkish Journal of Mathematics and Computer Science. 2020; 12(2): 76-85.
IEEE M. Bahşi and S. Solak , "On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers", Turkish Journal of Mathematics and Computer Science, vol. 12, no. 2, pp. 76-85, Dec. 2021, doi:10.47000/tjmcs.715052