On the recursive equivalence to Smith form of multivariate polynomial matrices

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

IMA Journal of Mathematical Control and Information Pub Date : 2022-09-30 DOI:10.1093/imamci/dnac023

Jinwang Liu, Dongmei Li

引用次数: 0

Abstract

The Smith form of an $n$-$D$ polynomial matrix plays an important role in many areas of mathematics and engineering. In this paper, we investigate the recursive equivalence problem of $n$-dimensional polynomial matrices, i.e. if diag$(1,B)$ is equivalent to diag$(1,1,C)$, is B equivalent to diag$(1,C)$? We give a negative answer to this question by explicitly constructing a four-dimensional polynomial matrix which is not equivalent to its Smith form.

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多元多项式矩阵的Smith形式的递推等价

$n$-$D$多项式矩阵的Smith形式在数学和工程的许多领域中起着重要的作用。本文研究了n维多项式矩阵的递推等价问题，即如果diag$(1,B)$等价于diag$(1,1,C)$，则B是否等价于diag$(1,C)$?我们通过显式构造一个不等价于史密斯形式的四维多项式矩阵给出了这个问题的否定答案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IMA Journal of Mathematical Control and Information 工程技术-应用数学

CiteScore

3.30

自引率

6.70%

发文量

审稿时长

>12 weeks

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