On the norms of r-circulant matrices with the hyperharmonic numbers
نویسندگان
چکیده
منابع مشابه
ON THE NORMS OF r-CIRCULANT MATRICES WITH THE HYPERHARMONIC NUMBERS
In this paper, we study norms of circulant matrices H = Circ(H 0 , H (k) 1 , . . . ,H (k) n−1) , H = Circ(H k , H (1) k , . . . ,H (n−1) k ) and r−circulant matrices Hr = Circr(H 0 ,H 1 , . . . ,H n−1) , Hr = Circr(H (0) k ,H (1) k , . . . ,H (n−1) k ) , where H (k) n denotes the n th hyperharmonic number of order r. Mathematics subject classification (2010): 15A60, 15B05, 11B99.
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In this paper, we present new upper and lower bounds for the spectral norms of the r-circulant matrices [Formula: see text] and [Formula: see text] whose entries are the biperiodic Fibonacci and biperiodic Lucas numbers, respectively. Finally, we obtain lower and upper bounds for the spectral norms of Kronecker and Hadamard products of Q and L matrices.
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Abstract In this paper, we consider the k -Fibonacci and k -Lucas sequences {Fk,n}n∈N and {Lk,n}n∈N . Let A = Cr(Fk,0, Fk,1, · · · , Fk,n−1) and B = Cr(Lk,0, Lk,1, · · · , Lk,n−1) be r -circulant matrices. Afterwards, we give upper and lower bounds for the spectral norms of matrices A and B. In addition, we obtain some bounds for the spectral norms of Hadamard and Kronecker products of these ma...
متن کاملON THE NORMS OF r–CIRCULANT MATRICES WITH THE HYPER–FIBONACCI AND LUCAS NUMBERS
In this paper, we study norms of circulant matrices F = Circ(F 0 , F (k) 1 , . . . ,F (k) n−1) , L = Circ(L 0 , L (k) 1 , . . . ,L (k) n−1) and r -circulant matrices Fr = Circr(F (k) 0 , F (k) 1 , . . . ,F (k) n−1) , Lr = Circr(L 0 , L (k) 1 , . . . ,L (k) n−1) , where F (k) n and L (k) n denote the hyper-Fibonacci and hyper-Lucas numbers, respectively. Mathematics subject classification (2010)...
متن کاملNorms of Circulant and Semicirculant Matrices with Horadam’s Numbers
In this paper, we obtain the spectral norm and eigenvalues of circulant matrices with Horadam’s numbers. Furthermore, we define the semicirculant matrix with these numbers and give the Euclidean norm of this matrix. 2000 Mathematics Subject Classification: 11B39; 15A36; 15A60; 15A18.
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2016
ISSN: 1846-579X
DOI: 10.7153/jmi-10-35