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Algorithms for finding the minimal polynomials and inverses of resultant matrices

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Abstract

In this paper, algorithms for computing the minimal polynomial and the common minimal polynomial of resultant matrices over any field are presented by means of the approach for the Gröbner basis of the ideal in the polynomial ring, respectively, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with resultant blocks over any field is given, which can be realized by CoCoA 4.0, an algebraic system over the field of rational numbers or the field of residue classes of modulo prime number. We get examples showing the effectiveness of the algorithms.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xidian University, 710071, Xi'an, P. R. China

    Shu-Ping Gao & San-Yang Liu

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  1. Shu-Ping Gao
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  2. San-Yang Liu
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Correspondence to Shu-Ping Gao.

Additional information

Foundation item: Shaanxi Natural Science Foundation of China (2002A12).

Gao Shuping received her BS and MS from Shaanxi Normal University and Xidian University in 1986 and 1994, respectively. Since 1986 she has been at the Xidian University. Since 2000 she has been at the Xidian University for Ph. D. Her research interests focus on the multi-objective programming, transportation network and the matrix theory.

Liu Sanyang received his BS, MS and Ph. D from Shaanxi Normal University, Xidian University and Xi'an Jiaotong University in 1982, 1984 and 1989, respectively. Since 1987 he has been at the Xidian University. His research interests focus on the multi-objective programming, combinatorial optimization, convex analysis and the matrix theory.

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Gao, SP., Liu, SY. Algorithms for finding the minimal polynomials and inverses of resultant matrices. JAMC 16, 251–263 (2004). https://doi.org/10.1007/BF02936166

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  • DOI: https://doi.org/10.1007/BF02936166

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