The Judgement for M-Matrices in Signal Processing

Abstract:

Special matrices play an important role in matrix analysis and matrix computation more and more. So it can give improvements by great progress obtained in the researches on special matrices in computational mathematics. In this paper, motivated by [4], we give a simple and convenient judging method which can be used to judge whether an nonnegative real matrix A is a M-matrix or not.

• Periodical: Applied Mechanics and Materials (Volumes 26-28)
• Pages: 422-425
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.26-28.422
• Online since: June 2010
• Authors: Ya Ning Lin
• Keywords: Inverse M-Matrix, M-Matrix, Signal Processing

References

[1] Yang Chuan-sheng, Yang Shang-jun, Closure Properties of Inverse M-matrices under Hadamard Product, Journal of Anhui University(Natural Sciences), Vol. 4(2000) , pp.15-20.

[2] Lou Xu-yang Cui Bao-tong, Exponential dissipativity of Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms, Vol. 4(2008), pp.619-922.

[3] Yang zhong-yuan, Fu Ying-ding, and Huang Ting-zhu, Some Properties of InverseM-Matrices and Their Applications, Joumal of UEST of China Vol. 34(2005), pp.713-716.

[4] Guo Xi-juan, Ji Nai-hua, Yao Hui-ping, The Judgement and Parallel Algorithm for Inverse M-matrixes , Journal of Beihua University, Vol. 45(2004), pp.97-103.

[5] A Berman, RJ Plemmons. Nonnegative Matrixes in the Mathematical Science[M]. New York: Academic Press, (1979).

[6] You Zhaoyong, Nonsingular M-matrix[M]. Wuhan: Huazhong University of Science and Technology Publishing House, (1983).

[7] Han Yin, The Property and Judgment of Inverse M-Matrixes, Journal of Huzhou Teachers College, Vol. 30(2008), pp.10-12.

[8] Deng Yihua, Problem of Cyclic Matrix Inversion, Journal of Hengyang �ormal University, 3(1995) 31-33.

[9] Hongkui Li, Xueting Liu and Wenling Zhao, Nonsingularity on Scaled Factor Circulant Matrices, International Journal of Algebra, Vol. 2, 2008, no. 18, 889 - 893.

[10] Zhaolin Jiang, Non singularity on r-circulant matrices, Mathematics in Practice and Theory, 2(1995) 52-58.

[11] Zhaolin Jiang, Non singularity on scaled factor circulant matrices, Journal of Baoji College of Arts and Science (�atural Science, 23 (2003) 5-7.

[12] Zhaolin Jiang, Liu Sanyang, The Fast Algorithm for Finding the Inverse and Generalized Inverse of Permutation Factor Circulant Matrix, �umerical Mathematics A Journal of Chinese Universities, 03(2003)227-234.

[13] Jiang Jiaqing, Two Simple Methods of Finding Inverse Matrix of Cyclic Matrix, Journal of Jiangxi Institute of Education(Comprehensive) , 3(2008) 5-6.

[14] Shen Guangxing, The Time Complexity of r-circulant Syestems [J], Journal Mathematical Research and Exposition, 4(1992), 595-598.

[15] Zhaolin Jiang, Zhou Zhangxin, Circulant Matrices, Chengdu Technology University Publishing Company, Chengdu, (1999).

[16] R.E. Cline, R.J. Plemmons and G. Worm, Generalized inverses of certain Toeplitz matrices, Linear Algebra and Its Applications, 8(1974), 25-33.

DOI: 10.1016/0024-3795(74)90004-4