On syzygy modules for polynomial matrices

Abstract In this paper, we apply the theory of multivariate polynomial matrices to the study of syzygy modules for a system of homogeneous linear equations with multivariate polynomial coefficients. Several interesting structural properties of syzygy modules are presented and illustrated with examples.

[1]  N. Bose.  Applied multidimensional systems theory , 1982 .

[2]  Lorenzo Robbiano,et al.  Computing minimal finite free resolutions , 1997 .

[3]  임종인,et al.  Gröbner Bases와 응용 , 1995 .

[4]  Ralf Fröberg,et al.  An introduction to Gröbner bases , 1997, Pure and applied mathematics.

[5]  B. Noble.  Applied Linear Algebra , 1969 .

[6]  H. M. Möller,et al.  New Constructive Methods in Classical Ideal Theory , 1986 .

[7]  Zhiping Lin.  On matrix fraction descriptions of multivariable linear n-D systems , 1988 .

[8]  N. Bose.  Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory , 1995 .

[9]  Dante C. Youla,et al.  Notes on n-Dimensional System Theory , 1979 .

[10]  Sun-Yuan Kung,et al.  New results in 2-D systems theory, part I: 2-D polynomial matrices, factorization, and coprimeness , 1977, Proceedings of the IEEE.

[11]  Ettore Fornasini,et al.  nD Polynomial Matrices with Applications to Multidimensional Signal Analysis , 1997, Multidimens. Syst. Signal Process..

[12]  Zhiping Lin,et al.  On primitive factorizations for n-D polynomial matrices , 1993, 1993 IEEE International Symposium on Circuits and Systems.

[13]  J. Guiver,et al.  Polynomial matrix primitive factorization over arbitrary coefficient field and related results , 1982 .

[14]  Thomas Kailath,et al.  Linear Systems , 1980 .

[15]  Zhiping Lin.  On primitive factorizations for 3-D polynomial matrices , 1992 .

[16]  Roberto La Scala,et al.  Strategies for Computing Minimal Free Resolutions , 1998, J. Symb. Comput..

[17]  Virendra Sule,et al.  Feedback Stabilization Over Commutative Rings: The Matrix Case , 1994 .

[18]  Sun-Yuan Kung,et al.  New Results in 2-D Systems Theory. Part III. Recursive Realization and Estimation Algorithms for 2-D Systems. , 1977 .