The characteristic equation of the matrix over min-plus algebra

IF 1.1 Q1 MATHEMATICS

JOURNAL OF INTERDISCIPLINARY MATHEMATICS Pub Date : 2023-01-01 DOI:10.47974/jim-1593

引用次数: 0

Abstract

Max-plus algebra is one of many idempotent semi-rings. The max-plus algebraic structure is semi field while the conventional algebra is a field. Because of their similar structure, various properties and concepts in the conventional algebra such as characteristic equations have max plus algebraic equivalence. The characteristic equation has been proved in the max-plus algebra. The other semi-field is min-plus algebra. Because of the structure in the min-plus algebra is also similar to the conventional algebra, the characteristic equation also has a min-plus algebraic equivalent. In this paper, it is discussed how to prove the characteristic equation of the matrix over conventional algebra into the min-plus algebra. The results are almost the same. The addition and multiplication operations in the conventional algebra are replaced by min and plus operations in the min-plus algebra. In addition, because of the min-plus algebra does not define the subtraction operation, the formulation of the characteristic equation of the matrix over min-plus algebra is not equal to zero.

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矩阵在最小加代数上的特征方程

极大正代数是许多幂等半环中的一个。极大正代数结构是半场，而常规代数结构是场。传统代数中的许多性质和概念，如特征方程，由于结构相似，具有极大的代数等价性。在max-plus代数中证明了特征方程。另一个半域是最小+代数。由于min- +代数中的结构也与常规代数相似，因此特征方程也具有min- +代数等价。本文讨论了如何将矩阵的特征方程在常规代数上证明为最小加代数。结果几乎是一样的。传统代数中的加法和乘法运算被最小加代数中的最小和加号运算所取代。另外，由于最小加代数没有定义减法运算，所以矩阵在最小加代数上的特征方程的表达式不等于零。

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

JOURNAL OF INTERDISCIPLINARY MATHEMATICS MATHEMATICS-

CiteScore

2.70

自引率

23.50%

发文量

141

期刊介绍： The Journal of Interdisciplinary Mathematics (JIM) is a world leading journal publishing high quality, rigorously peer-reviewed original research in mathematical applications to different disciplines, and to the methodological and theoretical role of mathematics in underpinning all scientific disciplines. The scope is intentionally broad, but papers must make a novel contribution to the fields covered in order to be considered for publication. Topics include, but are not limited, to the following: • Interface of Mathematics with other Disciplines • Theoretical Role of Mathematics • Methodological Role of Mathematics • Interface of Statistics with other Disciplines • Cognitive Sciences • Applications of Mathematics • Industrial Mathematics • Dynamical Systems • Mathematical Biology • Fuzzy Mathematics The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Editor-in-Chief’s discretion. Special issue proposals in cutting-edge and timely areas of research in interdisciplinary mathematical research are encouraged – please contact the Editor-in-Chief in the first instance.