数学
对偶(序理论)
基质(化学分析)
匡威
纯数学
乘法函数
组合数学
射影空间
公制(单位)
离散数学
投射试验
数学分析
几何学
材料科学
复合材料
运营管理
经济
作者
Christopher Hollings,Mark Kambites
出处
期刊:Journal of the London Mathematical Society
[Wiley]
日期:2012-05-28
卷期号:86 (2): 520-538
被引量:28
摘要
We give a complete description of Green's D relation for the multiplicative semigroup of all n-by-n tropical matrices. Our main tool is a new variant on the duality between the row and column space of a tropical matrix (studied by Cohen, Gaubert and Quadrat and separately by Develin and Sturmfels). Unlike the existing duality theorems, our version admits a converse, and hence gives a necessary and sufficient condition for two tropical convex sets to be the row and column space of a matrix. We also show that the matrix duality map induces an isometry (with respect to the Hilbert projective metric) between the projective row space and projective column space of any tropical matrix, and establish some foundational results about Green's other relations.
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