Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/60081


Title: 擴展型熱帶半環及熱帶矩陣之研究
On the Extended Tropical Semiring and Tropical Matrix Algebra
Authors: 徐昌祺
Contributors: 蔡炎龍
徐昌祺
Keywords: 熱帶矩陣
Date: 2009
Issue Date: 2013-09-04 15:15:24 (UTC+8)
Abstract: 熱帶幾何簡單的說是以熱帶半環為帶數結構所定義出的幾何學.如古典幾何學一樣,許多情況我們必須熟悉熱帶幾何中線性代數的性質.本篇論文是探討依熱帶半環上矩陣相關的問題.我們發現許多傳統矩陣有的性質在熱帶在熱帶矩陣並沒有相通的性質,但如果運用Izhakian定義的擴展型熱帶半環,許多定理就可以有類似傳統矩陣的結果.我們將介紹Izhakian的擴展型熱帶半環,定義擴展型熱帶矩陣,討論其和傳統矩陣,標準熱帶矩陣之差異,並探討其基本性質.
Reference: [1] Mike Develin, Francisco Santos, and Bernd Sturmfels. On the rank of a tropical matrix.
[2] Andreas Gathmann. Tropical algebraic geometry.
[3] Zur Izhakian. Tropical algebraic sets, ideals and an algebraic Nullstellensatz.
[4] Zur Izhakian. Tropical arithmetics and matrix algebra.
[5] Grigory Mikhalkin. Amoebas of algebraic varieties and tropical geometry.
[6] Grigory Mikhalkin. Enumerative tropical algebraic geometry in R2.
[7] Grigory Mikhalkin. Tropical geometry and its applications.
[8] Jurgen Richter-gebert, Bernd Sturmfels, and Thorsten Theobald. First steps in tropical geometry.
[9]David Speyer and Bernd Sturmfels. Tropical mathematics.
Description: 碩士
國立政治大學
應用數學系數學教學碩士在職專班
96972012
98
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0096972012
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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