Smith Form of Triangular Multivariate Polynomial Matrix

doi:10.1007/s11424-022-1289-z

Journal of Systems Science and Complexity ›› 2023, Vol. 36 ›› Issue (1): 151-164.DOI: 10.1007/s11424-022-1289-z

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Smith Form of Triangular Multivariate Polynomial Matrix

LIU Jinwang, WU Tao, LI Dongmei

School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China

Received:2021-08-11 Revised:2021-10-28 Online:2023-01-25 Published:2023-02-09
Supported by:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 11971161 and 11871207

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LIU Jinwang, WU Tao, LI Dongmei. Smith Form of Triangular Multivariate Polynomial Matrix[J]. Journal of Systems Science and Complexity, 2023, 36(1): 151-164.

The Smith form of a matrix plays an important role in the equivalence of matrix. It is known that some multivariate polynomial matrices are not equivalent to their Smith forms. In this paper, the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.

Key words: Degree-Lexicographical order, equivalence of matrix, multidimensional system, multivariate polynomial matrix, Smith form

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