In this study, we considered circulant matrices whose elements are Fibonacci polynomials. Then, we computed their determinants in two ways. In this content, we initially benefited from Chebyshev polynomials of the second kind. In the second way, we utilized some basic matrix operations. Moreover, we computed the inverse of these matrices in a general form. Furthermore, we found some kind of norms such as the Euclidean norm, upper and lower bounds for $ \|\mathcal{C}_n\|_2 $. In addition, we added some illustrative examples to make the results clear for the readers. In addition to these, we provide a MATLAB-R2023a code that writes the circulant matrix with the Fibonacci polynomial inputs, as well as computes Euclidean norms and bounds for their spectral norms.
Citation: Fatih Yılmaz, Aybüke Ertaş, Samet Arpacı. Some results on circulant matrices involving Fibonacci polynomials[J]. AIMS Mathematics, 2025, 10(4): 9256-9273. doi: 10.3934/math.2025425
In this study, we considered circulant matrices whose elements are Fibonacci polynomials. Then, we computed their determinants in two ways. In this content, we initially benefited from Chebyshev polynomials of the second kind. In the second way, we utilized some basic matrix operations. Moreover, we computed the inverse of these matrices in a general form. Furthermore, we found some kind of norms such as the Euclidean norm, upper and lower bounds for $ \|\mathcal{C}_n\|_2 $. In addition, we added some illustrative examples to make the results clear for the readers. In addition to these, we provide a MATLAB-R2023a code that writes the circulant matrix with the Fibonacci polynomial inputs, as well as computes Euclidean norms and bounds for their spectral norms.
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Fatih Yılmaz, Aybüke Ertaş, Samet Arpacı. Some results on circulant matrices involving Fibonacci polynomials[J]. AIMS Mathematics, 2025, 10(4): 9256-9273. doi: 10.3934/math.2025425
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