符号模式矩阵的谱任意性研究应用数学专业论文.docxVIP

? ? ? ? ? ? ? 论 ? ? ? ii ? ?束? 19 参⑧?③ 20 政卖????期??▲?论??????研??? 24 ?? 25 ? ? I ? ?? ?号??矩?????⑤合数?????????研??????▲???物??③ ?????????????多???具???????????????????-雅? ??④②?????号??和????号???????? ??章?述??号??矩?研??④?????????⑧?????论????? ??论? ??章②????n ≥ 8???号?????????号???????????都? ????号??? ??章将??-雅???④?展???号??????论?????号??????? ??号???????????都?????号??? ?????号?????号????????????? ? ? II ? ABSTRACT The sign pattern matrix is a very active research direction in the domain of combi- natorial mathematics in recent years,it has important application in many subjects such as economics?biology?chemistry?sociology?computer science and so on.In this paper,we mainly use the Nilpotent-Jacobian method to prove that a sign pattern matrix and a complex sign pattern matrix are spectrally arbitrary. In chapter 1,we introduce the history of development on the sign pattern matrices, some methods used in our paper and our research problems and main results. In chapter 2,we prove a sign pattern matrix of order n ≥ 8 is a minimally spectrally arbitrary sign pattern,and every superpattern of it is a spectrally arbitrary sign pattern. In chapter 3,we extend the Nilpotent-Jacobian method to prove a complex sign pattern matrix is a spectrally arbitrary sign pattern,and every superpattern of it is a spectrally arbitrary sign pattern. Key words?sign pattern,complex sign pattern,potentially nilpotent,spectrally arbitrary pattern ? ? PAGE 10 ? ??章 |言 § 1.1 ?号??矩?研??④? ⑤合数?????出②?后迅??展起????数??⑤???矩?论和???数? ?④?②?⑤合?????对⑤合?????述和???同???把⑤合论???和论② ?④??矩?????析??????????⑤合???20????????????? 数?通??企???和??????→?■????推?和???⑤合数???展??? ???????度?展和??起??⑤合数??◆多数??⑤?????多?联?和??? ???数?研????????????不????⑤合数?????????码和?码 ??物???③???物?????????????矩??论??????数????? 又??⑨具??????数??论??不??数???????⑤???????②?? ????????量?⑩??????数量???强?力?工具??????????? ?????矩?论???????????? ?号??矩????????合{+, ?, 0}?{1, ?1, 0}?矩??对?????矩?B = (bij )??其③????号sign(bij )?⑤??矩?→?B??号??矩??记?sgnB.?Qn▲? ?◆n??号??矩?⑤???合?对??A ∈ Qn????A??同?号?