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Journal articles on the topic 'Circulant matrices'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 March 2023

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1

Matsuki, Norichika. "Circulant Hadamard matrices and Hermitian circulant complex Hadamard matrices." International Mathematical Forum 16, no. 1 (2021): 19–22. http://dx.doi.org/10.12988/imf.2021.912166.

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2

Jiang, Zhaolin, and Dan Li. "The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant andg-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers." Abstract and Applied Analysis 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/931451.

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Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant andg-circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant matrix is discussed and the explicit determinant and the inverse matrices by constructing the transformation matrices are presented. Furthermore, the invertibility of the left circulant andg-circulant matrices is also studied. We obtain the explicit determinants and the inverse matrices of the left circulant andg-circulant matrices by utilizing the relationship between left circulant,g-circulant matrices and circulant matrix, respectively.

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3

Jiang, Zhaolin, Yanpeng Gong, and Yun Gao. "Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/375251.

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Circulant type matrices have become an important tool in solving differential equations. In this paper, we consider circulant type matrices, including the circulant and left circulant andg-circulant matrices with the sum and product of Fibonacci and Lucas numbers. Firstly, we discuss the invertibility of the circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices. Furthermore, the invertibility of the left circulant andg-circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the left circulant andg-circulant matrices by utilizing the relation between left circulant, andg-circulant matrices and circulant matrix, respectively.

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4

Liu, Li, and Zhaolin Jiang. "Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices." Abstract and Applied Analysis 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/169726.

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It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between left circulant,g-circulant matrices and circulant matrix, the invertibility of Tribonacci left circulant and Tribonaccig-circulant matrices is also discussed. Finally, the determinants and inverse matrices of these matrices are given, respectively.

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5

Pan, Hongyan, and Zhaolin Jiang. "VanderLaan Circulant Type Matrices." Abstract and Applied Analysis 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/329329.

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Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, andg-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaang-circulant matrix.

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6

Gong, Yanpeng, Zhaolin Jiang, and Yun Gao. "On Jacobsthal and Jacobsthal-Lucas Circulant Type Matrices." Abstract and Applied Analysis 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/418293.

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Circulant type matrices have become an important tool in solving fractional order differential equations. In this paper, we consider the circulant and left circulant andg-circulant matrices with the Jacobsthal and Jacobsthal-Lucas numbers. First, we discuss the invertibility of the circulant matrix and present the determinant and the inverse matrix. Furthermore, the invertibility of the left circulant andg-circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the left circulant andg-circulant matrices by utilizing the relation between left circulant,g-circulant matrices, and circulant matrix, respectively.

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7

Petrache, Horia I. "Generalized Circulant Matrices." Proceedings 2, no. 1 (January 3, 2018): 19. http://dx.doi.org/10.3390/proceedings2010019.

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8

Kra, Irwin, and Santiago R. Simanca. "On Circulant Matrices." Notices of the American Mathematical Society 59, no. 03 (March 1, 2012): 368. http://dx.doi.org/10.1090/noti804.

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9

Radhakrishnan, M., N. Elumalai, R. Perumal, and R. Arulprakasam. "Idempotent circulant matrices." Journal of Physics: Conference Series 1000 (April 2018): 012154. http://dx.doi.org/10.1088/1742-6596/1000/1/012154.

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10

Fan, Yun, and Hualu Liu. "Double circulant matrices." Linear and Multilinear Algebra 66, no. 10 (October 19, 2017): 2119–37. http://dx.doi.org/10.1080/03081087.2017.1387513.

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11

Arasu, Krishnasamy Thiru, and Alex J. Gutman. "Circulant weighing matrices." Cryptography and Communications 2, no. 2 (April 13, 2010): 155–71. http://dx.doi.org/10.1007/s12095-010-0025-z.

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12

Yao, Jin-jiang, and Zhao-lin Jiang. "The Determinants, Inverses, Norm, and Spread of Skew Circulant Type Matrices Involving Any Continuous Lucas Numbers." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/239693.

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We consider the skew circulant and skew left circulant matrices with any continuous Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the skew left circulant matrices by utilizing the relationship between skew left circulant matrices and skew circulant matrix, respectively. Finally, the four kinds of norms and bounds for the spread of these matrices are given, respectively.

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13

Park, Ju Yong, Jeong Su Kim, Ferenc Szollosi, and Moon Ho Lee. "The Toeplitz Circulant Jacket Matrices." Journal of the Institute of Electronics and Information Engineers 50, no. 7 (July 25, 2013): 19–26. http://dx.doi.org/10.5573/ieek.2013.50.7.019.

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14

Jiang, Zhaolin, Hongxia Xin, and Fuliang Lu. "Gaussian Fibonacci Circulant Type Matrices." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/592782.

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Circulant matrices have become important tools in solving integrable system, Hamiltonian structure, and integral equations. In this paper, we prove that Gaussian Fibonacci circulant type matrices are invertible matrices forn>2and give the explicit determinants and the inverse matrices. Furthermore, the upper bounds for the spread on Gaussian Fibonacci circulant and left circulant matrices are presented, respectively.

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15

Jiang, Xiaoyu, and Kicheon Hong. "Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/273680.

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Circulant matrix family is used for modeling many problems arising in solving various differential equations. The RSFPLR circulant matrices and RSLPFL circulant matrices are two special circulant matrices. The techniques used herein are based on the inverse factorization of polynomial. The exact determinants of these matrices involving Perrin, Padovan, Tribonacci, and the generalized Lucas number are given, respectively.

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16

Craigen, R., G. Faucher, R. Low, and T. Wares. "Circulant partial Hadamard matrices." Linear Algebra and its Applications 439, no. 11 (December 2013): 3307–17. http://dx.doi.org/10.1016/j.laa.2013.09.004.

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17

Hwang, Suk Geun. "Doubly stochastic circulant matrices." Discrete Mathematics 94, no. 1 (November 1991): 69–74. http://dx.doi.org/10.1016/0012-365x(91)90308-o.

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18

Daode, Huang. "On circulant Boolean matrices." Linear Algebra and its Applications 136 (July 1990): 107–17. http://dx.doi.org/10.1016/0024-3795(90)90022-5.

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19

Zheng, Yanpeng, and Sugoog Shon. "Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix." Abstract and Applied Analysis 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/760823.

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The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.

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20

Andrade, Enide, Cristina Manzaneda, Hans Nina, and María Robbiano. "Block matrices and Guo's index for block circulant matrices with circulant blocks." Linear Algebra and its Applications 556 (November 2018): 301–22. http://dx.doi.org/10.1016/j.laa.2018.07.015.

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21

Malakhov, S. S., and M. I. Rozhkov. "The construction of circulant matrices related to MDS matrices." Prikladnaya Diskretnaya Matematika, no. 56 (2022): 17–27. http://dx.doi.org/10.17223/20710410/56/2.

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The objective of this paper is to suggest a method of the construction of circulant matrices, which are appropriate for being MDS (Maximum Distance Separable) matrices utilising in cryptography. Thus, we focus on designing so-called bi-regular circulant matrices, and furthermore, impose additional restraints on matrices in order that they have the maximal number of some element occurrences and the minimal number of distinct elements. The reason to construct bi-regular matrices is that any MDS matrix is necessarily the bi-regular one, and two additional restraints on matrix elements grant that matrix-vector multiplication for the samples constructed may be performed efficiently. The results obtained include an upper bound on the number of some element occurrences for which the circulant matrix is bi-regular. Furthermore, necessary and sufficient conditions for the circulant matrix bi-regularity are derived. On the basis of these conditions, we developed an efficient bi-regularity verification procedure. Additionally, several bi-regular circulant matrix layouts of order up to 31 with the maximal number of some element occurrences are listed. In particular, it appeared that there are no layouts of order 32 with more than 5 occurrences of any element which yield a bi-regular matrix (and hence an MDS matrix).

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22

Jiang, Zhaolin, Jinjiang Yao, and Fuliang Lu. "On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/483021.

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Circulant and skew circulant matrices have become an important tool in networks engineering. In this paper, we consider skew circulant type matrices with any continuous Fibonacci numbers. We discuss the invertibility of the skew circulant type matrices and present explicit determinants and inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius) norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.

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23

Jiang, Zhaolin, and Yunlan Wei. "Skew Circulant Type Matrices Involving the Sum of Fibonacci and Lucas Numbers." Abstract and Applied Analysis 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/951340.

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Skew circulant and circulant matrices have been an ideal research area and hot issue for solving various differential equations. In this paper, the skew circulant type matrices with the sum of Fibonacci and Lucas numbers are discussed. The invertibility of the skew circulant type matrices is considered. The determinant and the inverse matrices are presented. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius) norm, the maximum row sum matrix norm, and bounds for the spread of these matrices are given, respectively.

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24

Xu, Wenai, and Zhaolin Jiang. "Norms and Spread of the Fibonacci and Lucas RSFMLR Circulant Matrices." Abstract and Applied Analysis 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/428146.

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Circulant type matrices have played an important role in networks engineering. In this paper, firstly, some bounds for the norms and spread of Fibonacci row skew first-minus-last right (RSFMLR) circulant matrices and Lucas row skew first-minus-last right (RSFMLR) circulant matrices are given. Furthermore, the spectral norm of Hadamard product of a Fibonacci RSFMLR circulant matrix and a Lucas RSFMLR circulant matrix is obtained. Finally, the Frobenius norm of Kronecker product of a Fibonacci RSFMLR circulant matrix and a Lucas RSFMLR circulant matrix is presented.

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25

Jiang, Zhaolin, Yanpeng Gong, and Yun Gao. "Invertibility and Explicit Inverses of Circulant-Type Matrices withk-Fibonacci andk-Lucas Numbers." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/238953.

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Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant-type matrices with thek-Fibonacci andk-Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which generalizes the results in Shen et al. (2011).

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26

Jitman, Somphong. "Determinants of some special matrices over commutative finite chain rings." Special Matrices 8, no. 1 (November 28, 2020): 242–56. http://dx.doi.org/10.1515/spma-2020-0118.

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AbstractCirculant matrices over finite fields and over commutative finite chain rings have been of interest due to their nice algebraic structures and wide applications. In many cases, such matrices over rings have a closed connection with diagonal matrices over their extension rings. In this paper, the determinants of diagonal and circulant matrices over commutative finite chain rings R with residue field 𝔽q are studied. The number of n × n diagonal matrices over R of determinant a is determined for all elements a in R and for all positive integers n. Subsequently, the enumeration of nonsingular n × n circulant matrices over R of determinant a is given for all units a in R and all positive integers n such that gcd(n, q) = 1. In some cases, the number of singular n × n circulant matrices over R with a fixed determinant is determined through the link between the rings of circulant matrices and diagonal matrices. As applications, a brief discussion on the determinants of diagonal and circulant matrices over commutative finite principal ideal rings is given. Finally, some open problems and conjectures are posted

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27

Mei, Ying. "A Method for Computing Logarithms of K-Circulant Matrices." Applied Mechanics and Materials 574 (July 2014): 661–64. http://dx.doi.org/10.4028/www.scientific.net/amm.574.661.

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In this paper, we present an efficient algorithm for computing the logarithms ofk-circulant matrices. And then we prove that nonsingulark-circulant matrices always has infinitely manyk-circulant logarithms.

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28

Jiang, Zhaolin, Tingting Xu, and Fuliang Lu. "Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/418194.

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The skew-circulant matrix has been used in solving ordinary differential equations. We prove that the set of skew-circulants with complex entries has an idempotent basis. On that basis, a skew-cyclic group of automorphisms and functional equations on the skew-circulant algebra is introduced. And different operators on linear vector space that are isomorphic to the algebra ofn×ncomplex skew-circulant matrices are displayed in this paper.

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29

Xu, Tingting, Zhaolin Jiang, and Ziwu Jiang. "Explicit Determinants of the RFPrLrR Circulant and RLPrFrL Circulant Matrices Involving Some Famous Numbers." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/647030.

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Circulant matrices may play a crucial role in solving various differential equations. In this paper, the techniques used herein are based on the inverse factorization of polynomial. We give the explicit determinants of the RFPrLrR circulant matrices and RLPrFrL circulant matrices involving Fibonacci, Lucas, Pell, and Pell-Lucas number, respectively.

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30

Banerjee, Debapratim, and Arup Bose. "Patterned sparse random matrices: A moment approach." Random Matrices: Theory and Applications 06, no. 03 (July 2017): 1750011. http://dx.doi.org/10.1142/s2010326317500113.

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We consider four specific [Formula: see text] sparse patterned random matrices, namely the Symmetric Circulant, Reverse Circulant, Toeplitz and the Hankel matrices. The entries are assumed to be Bernoulli with success probability [Formula: see text] such that [Formula: see text] with [Formula: see text]. We use the moment approach to show that the expected empirical spectral distribution (EESD) converges weakly for all these sparse matrices. Unlike the Sparse Wigner matrices, here the random empirical spectral distribution (ESD) converges weakly to a random distribution. This weak convergence is only in the distribution sense. We give explicit description of the random limits of the ESD for Reverse Circulant and Circulant matrices. As in the non-sparse case, explicit description of the limits appears to be difficult to obtain in the Toeplitz and Hankel cases. We provide some properties of these limits. We then study the behavior of the largest eigenvalue of these matrices. We prove that for the Reverse Circulant and Symmetric Circulant matrices the limit distribution of the largest eigenvalue is a multiple of the Poisson. For Toeplitz and Hankel matrices we show that the non-degenerate limit distribution exists, but again it does not seem to be easy to obtain any explicit description.

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31

ZHOU, JIANWEI, and ZHAOLIN JIANG. "SPECTRAL NORMS OF CIRCULANT-TYPE MATRICES WITH BINOMIAL COEFFICIENTS AND HARMONIC NUMBERS." International Journal of Computational Methods 11, no. 05 (October 2014): 1350076. http://dx.doi.org/10.1142/s021987621350076x.

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In this paper, we investigate spectral norms for circulant-type matrices, including circulant, skew-circulant, and g-circulant matrices. The entries are product of Binomial coefficients with Harmonic numbers. We obtain explicit identities for these spectral norms. Employing these approaches, we list some numerical tests to verify our results.

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32

Zhao, Wen Ling. "The Non-Singularity on the Level-2(r₁,r₂)-Circulant Matrices of Type (n₁,n₂)." Advanced Materials Research 108-111 (May 2010): 657–62. http://dx.doi.org/10.4028/www.scientific.net/amr.108-111.657.

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As special matrices, it is well known that the circulant matrices are very important. Various types of circulant matrices have been applied in such as signal dealing and oil exploration, and so on in recent years. In this paper, motivated by [1], we give some discriminations by using only the elements in the first row of the Level- -Circulant Matrices of Type and parameter on non singularity, and give two examples at last.

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33

Bottcher, A., S. M. Grudsky, and E. Ramirez de Arellano. "Approximating Inverse of Toeplitz Matrices by Circulant Matrices." Methods and Applications of Analysis 11, no. 2 (2004): 211–20. http://dx.doi.org/10.4310/maa.2004.v11.n2.a3.

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34

Mei, Ying. "Study on Some New Properties of k-Circulant Matrices." Applied Mechanics and Materials 536-537 (April 2014): 30–33. http://dx.doi.org/10.4028/www.scientific.net/amm.536-537.30.

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35

Zhou, Jianwei, Xiangyong Chen, and Zhaolin Jiang. "The Explicit Identities for Spectral Norms of Circulant-Type Matrices Involving Binomial Coefficients and Harmonic Numbers." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/518913.

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The explicit formulae of spectral norms for circulant-type matrices are investigated; the matrices are circulant matrix, skew-circulant matrix, andg-circulant matrix, respectively. The entries are products of binomial coefficients with harmonic numbers. Explicit identities for these spectral norms are obtained. Employing these approaches, some numerical tests are listed to verify the results.

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36

GUNASEKARAN, K., M. KAVITHA, and K. RAJESHKANNAN. "On Symmetric Circulant Fuzzy Matrices." Journal of Ultra Scientist of Physical Sciences Section A 30, no. 03 (March 2, 2018): 211–17. http://dx.doi.org/10.22147/jusps-a/300306.

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37

RADHAKRISHNAN, M., and N. ELUMALAI. "On k-Idempotent circulant matrices." Journal of Ultra Scientist of Physical Sciences Section A 30, no. 8 (August 2, 2018): 342–47. http://dx.doi.org/10.22147/jusps-a/300801.

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38

Kalman, Dan, and James E. White. "Polynomial Equations and Circulant Matrices." American Mathematical Monthly 108, no. 9 (November 2001): 821. http://dx.doi.org/10.2307/2695555.

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39

Brualdi, Richard A., and Michael W. Schroeder. "Circulant matrices and mathematical juggling." Art of Discrete and Applied Mathematics 1, no. 2 (July 26, 2018): #P2.01. http://dx.doi.org/10.26493/2590-9770.1235.c68.

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40

Bustomi and A. Barra. "Invertibility of some circulant matrices." Journal of Physics: Conference Series 893 (October 2017): 012012. http://dx.doi.org/10.1088/1742-6596/893/1/012012.

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41

Loganathan, C., and V. Pushpalatha. "Circulant Interval Valued Fuzzy Matrices." Annals of Pure and Applied Mathematics 16, no. 2 (February 1, 2018): 313–22. http://dx.doi.org/10.22457/apam.v16n2a8.

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42

Hariprasad, M. "Determinant of binary circulant matrices." Special Matrices 7, no. 1 (January 1, 2019): 92–94. http://dx.doi.org/10.1515/spma-2019-0008.

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43

Chen, Zhangchi. "On nonsingularity of circulant matrices." Linear Algebra and its Applications 612 (March 2021): 162–76. http://dx.doi.org/10.1016/j.laa.2020.12.010.

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44

Cureg, E., and A. Mukherjea. "Weak Convergence in Circulant Matrices." Journal of Theoretical Probability 18, no. 4 (October 2005): 983–1007. http://dx.doi.org/10.1007/s10959-005-7542-2.

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45

Zorzitto, Frank. "Groups acting on circulant matrices." Aequationes Mathematicae 48, no. 2-3 (October 1994): 294–305. http://dx.doi.org/10.1007/bf01832991.

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46

Hemasinha, Rohan, Nikhil R. Pal, and James C. Bezdek. "Iterates of fuzzy circulant matrices." Fuzzy Sets and Systems 60, no. 2 (December 1993): 199–206. http://dx.doi.org/10.1016/0165-0114(93)90346-j.

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47

Kalman, Dan, and James E. White. "Polynomial Equations and Circulant Matrices." American Mathematical Monthly 108, no. 9 (November 2001): 821–40. http://dx.doi.org/10.1080/00029890.2001.11919817.

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48

Tzoumas, Michael G. "On sign symmetric circulant matrices." Applied Mathematics and Computation 195, no. 2 (February 2008): 604–17. http://dx.doi.org/10.1016/j.amc.2007.05.006.

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49

Cauchois, Victor, and Pierre Loidreau. "On circulant involutory MDS matrices." Designs, Codes and Cryptography 87, no. 2-3 (August 22, 2018): 249–60. http://dx.doi.org/10.1007/s10623-018-0520-3.

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50

Sakuma, Tadashi, and Hidehiro Shinohara. "On circulant thin Lehman matrices." Electronic Notes in Discrete Mathematics 38 (December 2011): 783–88. http://dx.doi.org/10.1016/j.endm.2011.10.031.

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