On similarity problem of integral matrices

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:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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