文档介绍：安徽大学硕士学位论文矩阵行列式不等式与逆特征值问题姓名:蔡茜申请学位级别:硕士专业:应用数学指导教师:杨尚骏 ,一般的M,矩阵以及逆M一矩阵的一烘相关不等式,:在考虑给定的两个或三个特征值次序的情况下构造唯一的规范五对角线矩阵;由三个徐定的特征值和相应特缝囱量来构造嚷一的实对称三对角线矩簿葶鞋不可约实对称三对角线矩阵。文章中给出了前者商唯一解的充分条件以及聪者有难一解和有解(不雅一)的充要条件,. 关键词Hadamard不等式;Fischer不等式;Oppenheim不等式;M一矩阵 Abstract This paper consists oftwo thefirstpart,we shallprove several inequalities involving symmetric positive semidefinite,general M”matrices and inverse which are generalization of the classicalOppenheim’S Inequality forsyarmaetricpositive semidefinite matrices。Those main proofs ofthis part are based On noImegative。And inthesecond part,we consider thefollowing fourinverse eigenproblems:the reconstruction ofnormal fivemdiagonal matrix by two or three ordered eigenvalnes and corresponding eigenvectors,and the reconstruction ofrealsymmetric tridiagonal matrix and irreducible realsymmetric tridiagonal matrix by three eigenvalues and corresponding sufficientconditions for existence ofunique solution totheproblems are given here,and some necessary andsufficient conditions fortheexistence ofboth unique solutionandsolution(not unique)to the ,explicit expressions ofeach unique solution are given。Finally,numerical experiments are given。 Keywords Hadamard's inequality;Fischer’Sinequality;Oppenheim's inequality; M-matrices;InverseM-matrices;Hadamard product;Inverse eigenproblems;Real symmetric five·diagonal matrix;Real symmetric tridiagonal matrix;Irreducible realsymmetric tridiagonal matrix;Jacobi matrix;Eigenvalue andeigenvector. 第一拳零|畜与记号§,赞誉麓拧酚复短鬻记隽Mo(C),翳赢懿嚣羚安矩簿记受尉。(R).雌×行对称正宠矩阵、对称半砸蹙矩阵的全体分剐用P、,记蔻A怠0,筢薅A翡n令羚霰餐磊,磊,?,置。构疆紧畿念褥蠹A蕊滤,禳秀玎(零、穗如{(A),?,终}记为《黔,n除矩蹲A的第镪*1)除蹶序主子阵溆斑A(n). 避簸薄A鞫B辫Hadamard竣炎蠢。嚣, 菲对燕元全部葱菲匿数的方箨称为Z。矩洋。辫除Z,矩簿酶蕊会记为z, 鞠Z=p=(%)《M。(妁l搿F蠖魄Vi,歹蒜<攒》,f≠歹;.如暴矩阵A《Z虽A+‘为