Further results on n-D polynomial matrix factorizations

Multidimensional Systems and Signal Processing

Volumn 12, Issue 2, 2001, Pages 199-208

  Lin, Zhiping ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Matrix factorizations; n D polynomial matrices; Quillen Suslin theorem; Reduced minors; Zero primeness

Indexed keywords

COMPUTATIONAL METHODS; MATRIX ALGEBRA; SET THEORY;

GREATES COMMON DIVISOR (GCD); ZERO RIGHT PRIME (ZRP) FACTORIZATION;

POLYNOMIALS;

EID: 0035303501     PISSN: 09236082     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011192914450     Document Type: Article

References (13)

1. D. C. Youla and G. Gnavi, "Notes on n-dimensional system theory," IEEE Trans. Circuits Syst., vol. 26, Feb. 1979, pp. 105-111.
2. Z. Lin, "Notes on n-D polynomial matrix factorizations," Multidimensional Systems and Signal Processing, vol. 10, 1999, pp. 379-393.
3. N. K. Bose and C. Charoenlarpnopparut, "Multivariate matrix factorization: new results," presented at MTNS'98, padova, Italy, July, 1998.
4. C. Charoenlarpnopparut and N. K. Bose, "Multidimensional FIR filter bank design using Gröbner bases," IEEE Trans. Circuits Syst.-II: Analog and Digital Signal Proc., vol. 46, 1999, pp. 1475-1486.
5. M. Morf, B. C. Lévy and S. Y. Kung, "New results in 2-D systems theory, Part I: 2-D polynomial matrices, factorization and coprimeness," Proc. IEEE, vol. 65, June 1977, pp. 861-872.
6. J. P. Guiver and N. K. Bose, "Polynomial matrix primitive factorization over arbitrary coefficient field and related results," IEEE Trans. Circuits Syst., vol. 29, Oct. 1982, pp. 649-657.
7. B. C. Lévy, "2-D polynomial and rational matrices, and their applications for the modelling of 2-D dynamical systems," Ph.D. dissertation, Stanford Univ., Stanford, June 1981.
8. N. K. Bose, Applied Multidimensional Systems Theory, New York: Van Nostrand Reinhold, 1982.
9. D. C. Youla and P. F. Pickel, "The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices," IEEE Trans. Circuits Syst., vol. 31, 1984, pp. 513-518.
10. Z. Lin, "On matrix fraction descriptions of multivariable linear n-D systems," IEEE Trans. Circuits Syst., vol. 35, 1988, pp. 1317-1322.
11. S. Kleon and U. Oberst, "Transfer operators and state spaces for discrete multidimensional linear systems," Acta Applicandae Mathematicae, vol. 57, 1999, pp. 1-82.
12. F. R. Gantmacher, Theory of Matrices, vol. I and II, New York: Chelsea, 1959.
13. G. M. Greuel, G. Pfister, and H. Schonemann, Singular Reference Manual, Reports on Computer Algebra, No. 12, Centre of Algebra, University of Kaiserslautern, Germany. (Available from http://www.mathematik.uni-kl.de/~zca/Singular).