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On the norms of an \(r\)-circulant matrix with the generalized \(k\)-Horadam numbers. (English) Zbl 1373.11014
Summary: In this paper, we present new upper and lower bounds for the spectral norm of an \(r\)-circulant matrix \(H=C_r(H_{k,0}, H_{k,1}, H_{k,2},\ldots, H_{k, n-1})\) whose entries are the generalized \(k\)-Horadam numbers. Furthermore, we obtain new formulas to calculate the eigenvalues and determinant of the matrix \(H\).

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
15A15 Determinants, permanents, traces, other special matrix functions
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15B36 Matrices of integers
Full Text: DOI
[1] doi:10.1016/0148-9062(92)90514-Z · doi:10.1016/0148-9062(92)90514-Z
[2] doi:10.1016/j.amc.2003.08.126 · Zbl 1066.15029 · doi:10.1016/j.amc.2003.08.126
[3] doi:10.1016/j.amc.2010.03.140 · Zbl 1211.15029 · doi:10.1016/j.amc.2010.03.140
[4] doi:10.1016/j.camwa.2011.10.055 · Zbl 1238.11015 · doi:10.1016/j.camwa.2011.10.055
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