On the norms of an r-circulant matrix with the generalized k-Horadam numbers

Yazlık, Yasin; Taşkara, Necati

doi:10.1186/1029-242x-2013-394

Cited by 35 publications

(32 citation statements)

References 5 publications

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“…For example, we get the bounds for the spectral norms of geometric circulant matrices involving the generalized Fibonacci number and Lucas numbers [10]. On the other hand, we improve the results in reference [18], and we give new and better upper bounds for the norms of an r -circulant matrix involving the generalized k -Horadam numbers.…”

Section: Introductionmentioning

confidence: 76%

The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers

Shi

2018

J Inequal Appl

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In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-Horadam numbers, and we obtain some sharp estimations for them. We can also give a new estimation for the norms of a r-circulant matrix involving the generalized k-Horadam numbers.

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Section: Introductionmentioning

confidence: 76%

The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers

Shi

2018

J Inequal Appl

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“…A couple of years earlier Yazik and Taskara [13,Theorem 5] found even more general, yet a quite complicated, lower bound for Cr(h) .…”

Section: Chandoul [3 Theorem 22] Extended These Inequalities Tomentioning

confidence: 99%

On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix

et al. 2018

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“…There are many papers devoted to k-circulant matrices. We recommend the following papers: [5], [11], [18] and [19].…”

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confidence: 99%

Onk-circulant matrices (with geometric sequence)

Radičić

2015

Quaestiones Mathematicae

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To cite this article: Biljana Radičić (2015): On k-circulant matrices (with geometric sequence), Quaestiones Mathematicae, Abstract. Let k be a nonzero complex number. In this paper we show how the inverse of a nonsingular k-circulant matrix can be obtained. The method is used to determine the inverse of a nonsingular k-circulant matrix with geometric sequence. If k = 1, then we get the result presented in the paper A.C.F. Bueno, Right Circulant Matrices With Geometric Progression, Int. J. Appl. Math. Res. 1(4) (2012), 593-603. Also, we derive the Moore-Penrose inverse of a singular k-circulant matrix with geometric sequence. At the end of the paper, we illustrate the obtained results by examples. Mathematics Subject Classification (2010): 15B05, 15A09.

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On the norms of an r-circulant matrix with the generalized k-Horadam numbers

Abstract: In this paper, we present new upper and lower bounds for the spectral norm of an

Cited by 35 publications

References 5 publications

The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers

The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers

On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix

Onk-circulant matrices (with geometric sequence)

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