矩阵的矩阵

Therefore, in order to offer reference to readers, the paper systematically expound and prove the eigenvalue of special matrix that base on idempotent matrix, antiidempotent matrix, involutory matrix, anntiinvolutory matrix, nilpotent matrix, orthogonal matrix, polynomial matrix, the shape of , matrix, diagonal matrix, invertidle matrix, adjoint matrix, similar matrix, transposed matrix, numerical matrix, companion matrix, and practicality and superiority of the achievement was showed by some examples.

为此本文系统地阐述幂等矩阵，反幂等矩阵，对合矩阵，反对合矩阵，幂零矩阵，正交矩阵，多项式矩阵，形为：，矩阵，对角矩阵，可逆矩阵，伴随矩阵，相似矩阵，转置矩阵，友矩阵一系列特殊矩阵的特征值问题并加以证明，并通过一些具体例子展示所得成果的实用性和优越性。

It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想：(1)研究了Murthy等在[2]中提出的公开问题，即对任意的矩阵A，其扩充矩阵是否为Q_0-矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了Graves算法，证明了若A是双对称的P_0-矩阵时，LCP可由Graves算法给出；(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了Pang~-猜想，得到了只R_0-矩阵与Q-矩阵的二个等价条件，以及E_0∩Q-矩阵的一些性质；(3)研究了Danao在[25]中提出的Danao猜想，即，若A为P_0-矩阵，则，我们给出了反例证明了此猜想当n≥4时不成立，指出了Murthy等在[20]中的一些错误，得到n=2，3时，即[25]中定理3.2中A∈P_0的条件可以去掉。

Research Triangle Toeplitz matrix nature Diagonal extended to a non-zero constant for the formation of the matrix above 1.30 Toeplitz matrix.

研究三角Toeplitz矩阵性质，推广到对角线上为非零的一个常数的形如上三角Toeplitz矩阵的矩阵的情况。

This dissertation mainly investigated two frameworks of H-matrix, such as SPB framework consisting of integer Subscript matrix, Permutation matrix and Bidiagonal matrix and MSPT framework consisting of Masking matrix, sparse Subscript matrix, Permutation matrix and approximately lower Triangular array matrix.

本文主要研究了两种H矩阵的类随机框架结构模型，一是SPB框架，由整数下标矩阵、置换矩阵、双对角线矩阵构成；二是MSPT框架，由稀疏下标矩阵、模板矩阵、置换矩阵和近似下三角阵列矩阵构成。

Selfconjugate matrix, skewselfconjugate matrix, perselfconjugate matrix, skewperselfconjugate matrix, centrosymmetric matrix, skewcentrosymmetric matrix, bisymmetric matrix, and skewbisymmetric matrix over a ring with an involutorial antiautomorphism are defined. Significant criteria for matrices to be bisymmetric and skewbisymmetric are obtained.

在具有对合反自同构的环上定义了自共轭矩阵，斜自共轭矩阵，广自共轭矩阵，斜广自共轭矩阵，中心对称矩阵，斜中心对称矩阵，双对称矩阵和斜双对称矩阵，建立了双对称矩阵和斜双对称矩阵的重要判定定理。

When it approaches the triangular limit ,the non-diagonal reflection matrix of triangular statistical model is obtained.

本文得到了ZnBelavin模型反射矩阵的矩阵元表达式，在退化到三角极限后，得到了非对角的三角统计模型的反射矩阵。

Problem III Given find such thatProblem IV When Problem I or II or III is consistent, let Se denote the set of its solutions, for given , find , such thatwhere is Frobenius norm, S is Rn×p or a subset of Rn×p satisfying some constraint conditions, such as symmetric, skew-symmetric, centrosymmet-ric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric.

问题Ⅳ 设问题Ⅰ或Ⅱ或Ⅲ相容，且其解集合为SE，给定X0∈Rn×p，求X∈SE，使其中‖·‖为Frobenius范数，S为Rn×p或为Rn×p中满足某约束条件的矩阵集合，如对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵、双对称矩阵、对称次反对称矩阵等。

R~, find∈S_E, such that ProblemⅤGiven, find [X_1,X_2,…,X_l](where X_i∈S_i,i=1,2,…,l), such that A_1X_1B_1+A_2X_2B_2+…+A_lX_lB_l=C ProblemⅥWhen ProblemⅤis consistent, let SE denote the set of its solutions, for given,find, such that where||·|| is Frobenius norm, S and S_i are the matrix set satisfying some constraint conditions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric.

R~，求∈S_E，使得问题Ⅴ给定，求[X_1，X_2，…，X_l](其中X_i∈S_i，i=1，2，…，l)，使得 A_1X_1B_1+A_2X_2B_2+…+A_lX_lB_l=C 问题Ⅵ设问题Ⅴ相容，且其解集合为S_E，给定矩阵组，求，使得其中||·||为Frobenius范数，S，S_i为满足某种约束条件的矩阵集合，如对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵、双对称矩阵、对称次反对称矩阵等等。

By comparing the matrix theory over number field,we mainly discussed the quaternion matrix norm theory,the quaternionic determinant,the complex number expression of the quaternion matrix and the quarternion linear matrix equation.

通过对比一般域上矩阵理论，本文主要从四元数矩阵范数理论、四元数矩阵行列式、四元数矩阵的复表示以及四元数线性方程组和线性矩阵方程四个方面阐述了四元数矩阵理论。

Denotes the Frobenius norm, S is a subset of Rn×n. This master thesishas mainly studied centrosymmetric matrix set, centroskew symmetric matrix set,re?

为Frobenius范数， S为Rn×n中满足某约束条件的矩阵集合，本硕士论文主要研究了中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵、双对称矩阵、对称次反对称矩阵、对称正交对称矩阵、对称正交反对称矩阵。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。