Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers

Jiang, Xiaoyu; Hong, Kicheon

doi:10.1155/2014/273680

Cited by 24 publications

(17 citation statements)

References 21 publications

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“…In [14][15][16], RSFPLRcircfr(p T ) denotes the row skew first-plus-last right circulant matrix with the first row p T = [p 0 p 1 · · · p n−1 ], i.e., the matrix of the form…”

Section: Factor Circulant Decompositions Of Cuml Toeplitz Matricesmentioning

confidence: 99%

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

Jiang¹,

Hong²,

Fu³

2017

J. Nonlinear Sci. Appl.

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In this paper, we study mainly on a class of column upper-minus-lower (CUML) Toeplitz matrices without standard Toeplitz structure, which are " similar" to the Toeplitz matrices. Their (−1, −1)-cyclic displacements coincide with cyclic displacement of some standard Toeplitz matrices. We obtain the formula on representation for the inverses of CUML Toeplitz matrices in the form of sums of products of (−1, 1)-circulants and (1, −1)-circulants factor by constructing the corresponding displacement of the matrices. In addition, based on the relation between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula of CUML Hankel matrices can also be obtained.

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“…In [14][15][16], RSFPLRcircfr(p T ) denotes the row skew first-plus-last right circulant matrix with the first row p T = [p 0 p 1 · · · p n−1 ], i.e., the matrix of the form…”

Section: Factor Circulant Decompositions Of Cuml Toeplitz Matricesmentioning

confidence: 99%

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

Jiang¹,

Hong²,

Fu³

2017

J. Nonlinear Sci. Appl.

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“…The circulant matrices have in recent years been extended in many directions. The f (x)-circulant matrices are natural extension of circulant matrices, and can be found in [1][2][3][4][5][6][7][8][9][10][11][12]. The f (x)-circulant *Corresponding author: E-mail: jiangnan8767@163.com; matrix has a wide application, especially on the generalized cyclic codes [8].…”

Section: Introductionmentioning

confidence: 99%

“…The f (x)-circulant *Corresponding author: E-mail: jiangnan8767@163.com; matrix has a wide application, especially on the generalized cyclic codes [8]. The properties and structures of the (x n − x + 1)-circulant matrices [9][10][11][12], which are called row skew first-plus-last right (RSFPLR) circulant matrices, are better than those of the general f (x)-circulant matrices, so there are good methods for discriminations its non-singularity.…”

Section: Introductionmentioning

confidence: 99%

On Nonsingularity of RSFPLR Circulant Matrices

Cui

Jiang

2019

JAMCS

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In this paper, we discuss the non-singularity of a row skew rst-plus-last right (RSFPLR) circulant matrices with the rst row (a1; a2; : : : ; an),which is determined by entries of the first row. First,the suffient condition for the matrix to be nonsingular is that,there exists an element ai0 belonging to the first row,whose absolute value is greater than the sum of the corresponding power of 2 and the absolute values of the remaining (n − 1) elements, that is, $$|a_{i_0}|>\sum_{{i=1},{i\neq i_0}}^{n}2^{i-i_0}|a_i|.$$ Moreover, we derive other suffcient conditions for judging the non-singularity of the matrix.

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“…Jiang et al [11] gave the invertibility of circulant type matrices with the sum and product of Fibonacci and Lucas numbers and provided the determinants and the inverses of these matrices. In [13], Jiang and Hong gave the exact determinants of the RSFPLR circulant matrices and the RSLPFL circulant matrices involving Padovan, Perrin, Tribonacci, and the generalized Lucas numbers by the inverse factorization of polynomial. It should be noted that Jiang and Zhou [16] obtained the explicit formula for spectral norm of an r-circulant matrix whose entries in the first row are alternately positive and negative, and the authors [26] investigated explicit formulas of spectral norms for g-circulant matrices with Fibonacci and Lucas numbers.…”

Section: Introductionmentioning

confidence: 99%