On computing of positive integer powers for r-circulant matrices

Jiang, Zhaolin; Xin, Hongxia; Wang, Hongwei

doi:10.1016/j.amc.2015.05.022

Cited by 5 publications

(6 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Throughout this section, α and β are the roots of the equation x 2 − x − 1 = 0. First, we shall determine the eigenvalues of (12). Before that, let us recall that ψ is any n th root of a nonzero complex number k and ω is any primitive n th root of unity.…”

Section: Resultsmentioning

confidence: 99%

“…Theorem 2.2. Let L be the matrix as in (12). The eigenvalues of L are given by the following formulae:…”

Section: Resultsmentioning

confidence: 99%

“…There are many papers devoted to k-circulant matrices (especially to circulant and skew circulant matrices). Let us mention some of them: [5], [6], [10]− [12], [14], [15], [18]− [22], [27]− [32]. For example, the paper [11] is devoted to skew circulant matrices involving the sum of Fibonacci and Lucas numbers.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On k-circulant matrices with the Lucas numbers

Radičić¹

2018

Filomat

View full text Add to dashboard Cite

Let k be a nonzero complex number. In this paper, we determine the eigenvalues of a k-circulant matrix whose first row is (L 1 , L 2 ,. .. , L n), where L n is the n th Lucas number, and improve the result which can be obtained from the result of Theorem 7. [28]. The Euclidean norm of such matrix is obtained. Bounds for the spectral norm of a k-circulant matrix whose first row is (L −1 1 , L −1 2 ,. .. , L −1 n) are also investigated. The obtained results are illustrated by examples.

show abstract

Section: Resultsmentioning

confidence: 99%

“…Theorem 2.2. Let L be the matrix as in (12). The eigenvalues of L are given by the following formulae:…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

On k-circulant matrices with the Lucas numbers

Radičić¹

2018

Filomat

View full text Add to dashboard Cite

show abstract

“…The powers of matrices are thus of considerable importance. Computing the integer powers of circulant matrices depending on Chebyshev polynomials recently has been a very attractive problem [6]- [13]. For example, Rimas obtained a general expression for the entries of the r th power (r ∈ N) of the n × n real symmetric circulant circ n (0, 1, 0, .…”

Section: Introductionmentioning

confidence: 99%

Circulant $m$-Diagonal Matrices Associated with Chebyshev Polynomials

Öteleş

2021

Fundamental Journal of Mathematics and Applications

View full text Add to dashboard Cite

In this study, we deal with an m banded circulant matrix, generally called circulant mdiagonal matrix. This special family of circulant matrices arise in many applications such as prediction, time series analysis, spline approximation, difference solution of partial differential equations, and so on. We firstly obtain the statements of eigenvalues and eigenvectors of circulant m-diagonal matrix based on the Chebyshev polynomials of the first and second kind. Then we present an efficient formula for the integer powers of this matrix family depending on the polynomials mentioned above. Finally, some illustrative examples are given by using maple software, one of computer algebra systems (CAS).

show abstract

“…Necessary and sufficient conditions for a complex square matrix to be a k-circulant matrix were presented by R. E. Cline, R. J. Plemmons and G. Worm in the paper [5] (see Lemmas 2 and 3 in [5]). In the paper [8], the authors showed how C q can be obtained, where C is a matrix of the form (1.1) and q is a positive integer greater than 1.…”

Section: Introductionmentioning

confidence: 99%

On k-circulant matrices involving geometric sequence

Radičić¹

2018

HJMS

View full text Add to dashboard Cite

In this paper we consider a k-circulant matrix with geometric sequence, where k is a nonzero complex number. The eigenvalues, the determinant, the Euclidean norm and bounds for the spectral norm of such matrix are investigated. The method for obtaining the inverse of a nonsingular k-circulant matrix, was presented in [?]. A generalization of that method is given in this paper, and using it, the inverse of a nonsingular k-circulant matrix with geometric sequence is obtained. The Moore-Penrose inverse of a singular k-circulant matrix with geometric sequence is determined in a different way than the way using in [?].

show abstract

On computing of positive integer powers for r-circulant matrices

Cited by 5 publications

References 17 publications

On k-circulant matrices with the Lucas numbers

On k-circulant matrices with the Lucas numbers

Circulant $m$-Diagonal Matrices Associated with Chebyshev Polynomials

On k-circulant matrices involving geometric sequence

Contact Info

Product

Resources

About