撤稿：含Pell与Pell-Lucas数之积的斜循环矩阵的行列式及其性质

doi:10.12677/AAM.2020.912247

期刊菜单

撤稿：含Pell与Pell-Lucas数之积的斜循环矩阵的行列式及其性质
Determinants and Properties of Skew Circulant Matrices Involving the Product of Pell Numbers and Pell-Lucas Numbers

DOI: 10.12677/AAM.2020.912247, PDF, HTML, 下载: 652 浏览: 899
作者: 李笑丽, 何承源, 雷林：西华大学理学院，四川成都
关键词: 行列式；范数；Pell数列；Pell-Lucas数列；斜循环矩阵；Determinant； Norm； Pell Number； Pell-Lucas Number； Skew Circulant Matrix

摘要: 撤稿声明：“含Pell与Pell-Lucas数之积的斜循环矩阵的行列式及其性质”一文刊登在2020年12月出版的《应用数学进展》2020年第9卷第12期第2129-2138页上。因该文研究内容另作他用，作者主动申请撤稿。根据国际出版流程，编委会现决定撤除此稿件，保留原出版出处：李笑丽, 何承源, 雷林. 含Pell与Pell-Lucas数之积的斜循环矩阵的行列式及其性质[J]. 应用数学进展, 2020, 9(12): 2129-2138. https://doi.org/10.12677/AAM.2020.912247

Abstract:

文章引用：李笑丽, 何承源, 雷林. 撤稿：含Pell与Pell-Lucas数之积的斜循环矩阵的行列式及其性质[J]. 应用数学进展, 2020, 9(12): 2129-2138. https://doi.org/10.12677/AAM.2020.912247

参考文献

[1] Hellings, C. and Utschick, W. (2015) Block-Skew-Circulant Matrices in Complex-Valued Signal Processing. IEEE Transactions on Signal Process, 63, 2093-2107.
https://doi.org/10.1109/TSP.2015.2395992

[2] Huckle, T. (1992) Circulant and Skewcirculant Matrices for Solving Toeplitz Matrix Problems. SIAM Journal on Matrix Analysis & Applications, 13, 767-777.
https://doi.org/10.1137/0613048

[3] Fu, D.Q., Jiang, Z.L., Cui, Y.F. and Jhang, S.T. (2014) New Fast Algorithm for Optimal Design of Block Digital Filters by Skew-Cyclic Convolution. IET Signal Processing, 8, 633-638.
https://doi.org/10.1049/iet-spr.2013.0384

[4] Gao, Y., Jiang, Z.L. and Gong, Y.P. (2013) On the Determinants and Inverses of Skew Circulant and Skew Left Circulant Matrices with Fibonacci and Lucas Numbers. WSEAS Transactions on Mathematics, 12, 472-481.

[5] Jiang, X. and Hong, K. (2014) Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers. Abstract and Applied Analysis, 2014, Article ID: 273680.
https://doi.org/10.1155/2014/273680

[6] Yazlik, Y. and Taskara, N. (2013) On the Norms of an r-Circulant Matrix with the Generalized k-Horadam Numbers. Journal of Inequalities & Applications, 2013, Article No. 394.
https://doi.org/10.1186/1029-242X-2013-394

[7] Yao, J.J. and Sun, J.X. (2018) Explicit Determinants and Inverses of Skew Circulant and Skew Left Circulant Matrices with the Pell-Lucas Numbers. Journal of Advances in Mathematics and Computer Science, 26, 1-16.
https://doi.org/10.9734/JAMCS/2018/38768

[8] Solak, S. (2005) On the Norms of Circulant Matrices with the Fibonacci and Lucas Numbers. Applied Mathematics and Computation, 160, 125-132.
https://doi.org/10.1016/j.amc.2003.08.126

[9] Shen, S.Q., Cen, J.M. and Hao, Y. (2011) On the Determinants and Inverses of Circulant Matrices with Fibonacci and Lucas Numbers. Applied Mathematics and Computation, 217, 9790-9797.
https://doi.org/10.1016/j.amc.2011.04.072

[10] Zheng, Y.P. and Shon, S. (2015) Exact Determinants and Inverses of Generalized Lucas Skew Circulant Type Matrices. Applied Mathematics and Computation, 270, 105-113.
https://doi.org/10.1016/j.amc.2015.08.021

[11] Bozkurt, D. and Yılmaz, F. (2012) On the Determinants and Inverses of Circulant Matrices with Pell and Pell-Lucas Numbers. Mathematics: Numerical Analysis. arXiv:1201.6061.

[12] Li, J., Jiang, Z.L. and Lu, F.L. (2014) Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers. Abstract and Applied Analysis, 2014, Article ID: 381829.
https://doi.org/10.1155/2014/381829

[13] Wei, Y.L., Zheng, Y.P., Jiang, Z.L. and Shon, S. (2020) Determinants, Inverses, Norms, and Spreads of Skew Circulant Matrices Involving the Product of Fibonacci and Lucas Numbers. Journal of Mathematics and Computer Science, 20, 64-78.
https://doi.org/10.22436/jmcs.020.01.08

[14] Wei, Y.L., Zheng, Y.P., Jiang, Z.L. and Shon, S. (2020) Determinants, Norms and Spreads of Skew Circulant Matrices Involving the Sum of Pell and Pell-Lucas Numbers. Advances and Applications in Discrete Mathematics, 23, 13-24.
https://doi.org/10.17654/DM023010013

[15] Lu, F. and Jiang, Z. (1994) The Sum and Product of Fibonacci Numbers and Lucas Numbers, Pell Numbers and Pell-Lucas Numbers Representation by Matrix Method. WSEAS Transactions on Mathematics, 12, 449-458.

[16] Karner, H., Schneid, J. and Ueberhuber, C.W. (2003) Spectral Decomposition of Real Circulant Matrices. Linear Algebra Applications, 367, 301-311.
https://doi.org/10.1016/S0024-3795(02)00664-X

[17] Sharma, R. and Kumar, R. (2013) Remark on Upper Bounds for the Spread of a Matrix. Linear Algebra and its Applications, 438, 4359-4362.
https://doi.org/10.1016/j.laa.2013.01.018

[18] Johnson, C.R., Kumar, R. and Wolkowicz, H. (1985) Lower Bounds for the Spread of a Matrix. Linear Algebra and its Applications, 71, 161-173.
https://doi.org/10.1016/0024-3795(85)90244-7

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[1]	Hellings, C. and Utschick, W. (2015) Block-Skew-Circulant Matrices in Complex-Valued Signal Processing. IEEE Transactions on Signal Process, 63, 2093-2107. https://doi.org/10.1109/TSP.2015.2395992
[2]	Huckle, T. (1992) Circulant and Skewcirculant Matrices for Solving Toeplitz Matrix Problems. SIAM Journal on Matrix Analysis & Applications, 13, 767-777. https://doi.org/10.1137/0613048
[3]	Fu, D.Q., Jiang, Z.L., Cui, Y.F. and Jhang, S.T. (2014) New Fast Algorithm for Optimal Design of Block Digital Filters by Skew-Cyclic Convolution. IET Signal Processing, 8, 633-638. https://doi.org/10.1049/iet-spr.2013.0384
[4]	Gao, Y., Jiang, Z.L. and Gong, Y.P. (2013) On the Determinants and Inverses of Skew Circulant and Skew Left Circulant Matrices with Fibonacci and Lucas Numbers. WSEAS Transactions on Mathematics, 12, 472-481.
[5]	Jiang, X. and Hong, K. (2014) Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers. Abstract and Applied Analysis, 2014, Article ID: 273680. https://doi.org/10.1155/2014/273680
[6]	Yazlik, Y. and Taskara, N. (2013) On the Norms of an r-Circulant Matrix with the Generalized k-Horadam Numbers. Journal of Inequalities & Applications, 2013, Article No. 394. https://doi.org/10.1186/1029-242X-2013-394
[7]	Yao, J.J. and Sun, J.X. (2018) Explicit Determinants and Inverses of Skew Circulant and Skew Left Circulant Matrices with the Pell-Lucas Numbers. Journal of Advances in Mathematics and Computer Science, 26, 1-16. https://doi.org/10.9734/JAMCS/2018/38768
[8]	Solak, S. (2005) On the Norms of Circulant Matrices with the Fibonacci and Lucas Numbers. Applied Mathematics and Computation, 160, 125-132. https://doi.org/10.1016/j.amc.2003.08.126
[9]	Shen, S.Q., Cen, J.M. and Hao, Y. (2011) On the Determinants and Inverses of Circulant Matrices with Fibonacci and Lucas Numbers. Applied Mathematics and Computation, 217, 9790-9797. https://doi.org/10.1016/j.amc.2011.04.072
[10]	Zheng, Y.P. and Shon, S. (2015) Exact Determinants and Inverses of Generalized Lucas Skew Circulant Type Matrices. Applied Mathematics and Computation, 270, 105-113. https://doi.org/10.1016/j.amc.2015.08.021
[11]	Bozkurt, D. and Yılmaz, F. (2012) On the Determinants and Inverses of Circulant Matrices with Pell and Pell-Lucas Numbers. Mathematics: Numerical Analysis. arXiv:1201.6061.
[12]	Li, J., Jiang, Z.L. and Lu, F.L. (2014) Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers. Abstract and Applied Analysis, 2014, Article ID: 381829. https://doi.org/10.1155/2014/381829
[13]	Wei, Y.L., Zheng, Y.P., Jiang, Z.L. and Shon, S. (2020) Determinants, Inverses, Norms, and Spreads of Skew Circulant Matrices Involving the Product of Fibonacci and Lucas Numbers. Journal of Mathematics and Computer Science, 20, 64-78. https://doi.org/10.22436/jmcs.020.01.08
[14]	Wei, Y.L., Zheng, Y.P., Jiang, Z.L. and Shon, S. (2020) Determinants, Norms and Spreads of Skew Circulant Matrices Involving the Sum of Pell and Pell-Lucas Numbers. Advances and Applications in Discrete Mathematics, 23, 13-24. https://doi.org/10.17654/DM023010013
[15]	Lu, F. and Jiang, Z. (1994) The Sum and Product of Fibonacci Numbers and Lucas Numbers, Pell Numbers and Pell-Lucas Numbers Representation by Matrix Method. WSEAS Transactions on Mathematics, 12, 449-458.
[16]	Karner, H., Schneid, J. and Ueberhuber, C.W. (2003) Spectral Decomposition of Real Circulant Matrices. Linear Algebra Applications, 367, 301-311. https://doi.org/10.1016/S0024-3795(02)00664-X
[17]	Sharma, R. and Kumar, R. (2013) Remark on Upper Bounds for the Spread of a Matrix. Linear Algebra and its Applications, 438, 4359-4362. https://doi.org/10.1016/j.laa.2013.01.018
[18]	Johnson, C.R., Kumar, R. and Wolkowicz, H. (1985) Lower Bounds for the Spread of a Matrix. Linear Algebra and its Applications, 71, 161-173. https://doi.org/10.1016/0024-3795(85)90244-7