發(fā)布時間：2018-03-25 03:10

  本文選題：K-Hermite環(huán)　切入點：唯一分解環(huán)　出處：《湖南科技大學(xué)》2014年碩士論文

【摘要】：唯一分解環(huán)上矩陣的分解問題在符號計算與控制論、網(wǎng)絡(luò)編碼、電路、信號處理、多維系統(tǒng)等工程計算方面起著重要的作用。許多環(huán)R上矩陣分解問題與環(huán)R是否具有Hermite性質(zhì)密切相關(guān),研究唯一分解環(huán)上矩陣分解問題時先要研究了它的Hermite性質(zhì),我們對唯一分解環(huán)的Hermite性質(zhì),唯一分解環(huán)上矩陣的分解等問題進行了一些有意義的探討,取得了一些初步的結(jié)果。其中重要而有意義結(jié)果；1.因K-Hermite環(huán)上可能存在零因子,所以此環(huán)上矩陣分解問題的研究較為不便,本文主要根據(jù)K-Hermite環(huán)的定義得出此環(huán)上互素的兩個元素b,v,對此環(huán)上任意c,若有b|(Vc),則b|c,從而得出若M=p(G),則M有核表示的充分條件。2.對于K-Hermite環(huán)R,A∈Rl×n(l≤n), rank(A)≥l-1,d是A的所有,×,級子式的任一極大公因式,則A可嵌入到矩陣(A N),且det(A N)=d。3.對于d-Hermite環(huán)R,F∈Rl×m(l≤m)是ZLP矩陣,則F可嵌入一個m×m階可逆矩陣A中,這些結(jié)論為此環(huán)上矩陣分解的研究打下基礎(chǔ)。 前人研究了多元(變)多項式環(huán)上矩陣分解問題,而多元多項式環(huán)是一類特殊的唯一分解環(huán),我們探討了對于唯一分解環(huán),關(guān)于非正則因子是否也可以得出矩陣分解的相關(guān)結(jié)論,通過努力,舉出了一個反例,同時也得到了一些其它有價值的結(jié)果。 對于Lin-Bose問題,在滿秩情況下Li u給出簡單易懂的證明方法,本文最后研究了在唯一分解環(huán)上非滿秩情況下的Lin-Bose問題。
[Abstract]:The decomposition problems of matrices over a unique decomposition ring are symbolic computation and cybernetics, network coding, circuits, signal processing, Many matrix decomposition problems over a ring R are closely related to whether the ring R has Hermite property. The Hermite property of matrix decomposition problem over a unique factorization ring should be studied first when we study the matrix decomposition problem over a unique factorization ring. In this paper, we discuss the Hermite property of the unique decomposition ring and the decomposition of the matrix over the unique factorization ring, and obtain some preliminary results, among which the important and meaningful result is 1.Because there may be zero divisors on the K-Hermite ring, Therefore, it is inconvenient to study the matrix decomposition problem over this ring. In this paper, based on the definition of K-Hermite ring, we obtain two elements of coprime on this ring, b ~ (v). For any c on this ring, if there is b ~ (Vc), then b _ (c), we obtain the sufficient condition that M has kernel representation if M ~ (?) p ~ (1), then M is a sufficient condition of kernel representation. For K-Hermite ring R _ (1) A 鈭，

本文編號：1661268