English  |  正體中文  |  简体中文  |  Items with full text/Total items : 66984/66984 (100%) Visitors : 22605033      Online Users : 181
 Scope All of NCUIR 理學院    數學研究所       --博碩士論文 Tips: please add "double quotation mark" for query phrases to get precise resultsplease goto advance search for comprehansive author search Adv. Search
 NCU Institutional Repository > 理學院 > 數學研究所 > 博碩士論文 >  Item 987654321/79639

 Please use this identifier to cite or link to this item: `http://ir.lib.ncu.edu.tw/handle/987654321/79639`

 Title: On similarity problem of integral matrices Authors: 陳穎融;Chen, Ying-jung Contributors: 數學系 Keywords: similarity problem Date: 2018-12-17 Issue Date: 2019-04-02 15:09:42 (UTC+8) Publisher: 國立中央大學 Abstract: 在這篇論文中，我們會先介紹矩陣的canonical form，並利用它來解決2-by-2整數矩陣的相似問題。除了canonical forms之外，我們也會找出generators of the stabilizers of the canonical forms，目的是為了解決3-by-3整數矩陣的相似問題。在應用方面，相似問題能幫助我們算出ideal class number of a quadratic algebra over rational number field Q。最後，在論文中也提供了計算canonical form、判斷矩陣是否相似以及算出判斷矩陣是否相似以及算出ideal classes numbers of quadratic Z-orders的程式碼。;In this thesis, we first introduce the canonical forms and solve the similarity problem of the case of 2-by-2 integral matrices. One direct application is to compute the ideal class number of a quadratic algebra over Q. We also determine the generators of the stabilizers of the canonical forms for 2-by-2 integral matrices, which enables us to solve the similarity problem of 3-by-3 integral matrices with reducible characteristic polynomials. Furthermore, we provide the codes(using Sagemath) for computing the canonical form of a given matrix, determining whether two given matrices are similar or not, and computing the ideal classes numbers of quadratic Z-orders. Appears in Collections: [數學研究所] 博碩士論文

Files in This Item:

File Description SizeFormat
index.html0KbHTML31View/Open