| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 陳穎融 | zh_TW |
| DC.creator | Ying-jung Chen | en_US |
| dc.date.accessioned | 2018-12-17T07:39:07Z | |
| dc.date.available | 2018-12-17T07:39:07Z | |
| dc.date.issued | 2018 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=105221004 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.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。 | zh_TW |
| dc.description.abstract | 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. | en_US |
| DC.subject | similarity problem | zh_TW |
| DC.title | On similarity problem of integral matrices | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |