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We study some ratios related to hyper-Horadam numbers such as Wnr/Wn-1r while n→∞ by using a symmetric algorithm obtained by the recurrence relation ank=ank-1+an-1k, where Wnr is the nth hyper-Horadam number. Also, we give some special cases of these ratios such as the golden ratio and silver ratio.

Abstract. In this paper, we study norms of circulant matrices F = Circ(F

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In this study, we have established the bounds for the \(\ell_p \) norms and the Euclidean norm of almost GCD Cauchy-Toeplitz, almost GCD Cauchy-Hankel and GCD matrices, respectively.

In this paper, we compute the spectral norms of r− circulant matrices with the hyper-Fibonacci and hyper-Lucas numbers of the forms) and their Hadamard and Kronecker products. For this, we firstly compute the spectral and Euclidean norms of circulant matrices of the forms. Moreover, we give some examples related to special cases of our results.

Let Cn, Tn and Hn denote almost circulant, Cauchy-ToeplitZ and Cauchy-Hankel matrices, respectively. We find some upper bounds for \(\ell_p\) matrix norm and \(\ell_p\) operator norm of this matrices. Moreover, we give some results for Kronecker products Cn\(\otimes\)Tn and Cn\(\otimes\)Hn.