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Finally, a hospital viscosity of plasma diagnostic system is optimized by adjoint matrix method and M-P generalized inverse matrix method of MTS. The results show that adjoint matrix method can't select effective variables and M-P generalized inverse matrix method is robust.

最后，利用马氏田口伴随矩阵法和M-P广义逆矩阵法对某医院现阶段血粘度诊断系统进行优化，说明伴随矩阵法在选择有效变量时存在的问题和M-P广义逆矩阵法的稳健性。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

From the history of Matrix and Transformation and the development of curriculum at home and abroad, putting matrix combined with the transformation, and orienting the study in 2×2 rank matrix, boosting matrix up the geometrical visualization as a algebra objects are a new perspective on knowing matrix.

从矩阵和变换的历史发展过程和国内外矩阵和变换的课程设置来看，把矩阵与变换相结合，并定位在2×2阶上研究矩阵，增强作为代数对象的矩阵的几何直观性，是认识矩阵的一个新视角。

A way of TOPSIS for multiple target decision is applied to space with matrix elements,and we can make comprehensive evaluation of information system according to the relative distance between evaluation index matrix and best solution matrix and worst solution matrix.

再将多目标决策中的逼近理想解法应用到以矩阵为元素的空间中，按照与理想解和负理想解的相对接近度去对信息系统作出综合评价。

TOPSIS for multiple target decision is applied to space with matrix elements, and we can make comprehensive evaluation of enterprise economic benefit according to the relative distance between evaluation index matrix,best solution matrix and worst solution matrix.

将多目标决策中的逼近理想解法应用到以矩阵为元素的空间中，按照评价点与理想解和负理想解的相对接近度对企业经济效益作出综合评价。

We make the following assumption for When 2 is positive definite matrix, different estimators about matrix of regression coefficients and inefficiency of Least squares estimate have been discussed in many documents. Considered 2 is nonnegative definite matrix, this thesis derives Best linear unbiased Estimate of parameter matrix B and estimable parameter function KBL under the meaning of matrix nonnegative definite and the property of maximum probability of BLUE is investigated.

当∑＞0时，众多文献讨论了回归系数阵的各种估计及LSE的有效性，本文考虑了当∑≥0的情形，给出了回归系数阵B及其可估参数函数KBL的在矩阵非负定意义下的最优估计，研究了它的一个最大概率性质，并且讨论了最小二乘估计成为最佳线性无偏估计的充分必要条件，在此基础上给出了均值矩阵的最小二乘估计与BLUE的偏差估计，定义了LSE相对于BLUE的一个相对效率，并给出了它的界。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

In chapter one,we discuss tournament matrices that can not end in tie and theyare(0,1)-matrices,we first obtain a better lower bound for the number of regulartournament matrices,then we discuss the payoff matrix of tournament matrix,obtainsome properties of positive tournament matrices,a correlation between the spectralof a tournament matrix and its payoff matrix.We find serveal conditions that areequivalaent to a tournament matrix having 1 as its a eigenvalue.

第一章讨论不允许平局的竞赛矩阵-（0，1）-矩阵，得到了正则竞赛矩阵数目的一个下界，它改进了文献〓中已有的结果；在文献〓的基础上进一步讨论了正竞赛矩阵的性质，给出了利用已知平衡向量构造新平衡向量的方法；讨论了竞赛矩阵和它的支付矩阵的特征值之间的关系；指出了文献〓中的一个错误，回答了文献〓中的一个公开问题，得到了整数1为竞赛矩阵的特征值的充要条件及这种矩阵的谱根与得分向量之间的关系。

At first, the paper quote a kind of special matrix ---sign symmetric matrix , anti sign symmetric matrix , weakly sign symmetric matrix and introduced some important results in spectral property about them from some bibliographies. And then, the paper extended the formerly results and gave more general conclusions about spectral property of sign symmetric matrix.

本文首先引入了一类特殊矩阵的概念——符号对称矩阵，反符号对称矩阵以及弱符号对称矩阵，在相关文献中对这类矩阵谱特征的已经有了一些结论，本文在前人研究的基础上将相关结论做了进一步的推广，得出了有关这类符号对称矩阵谱特征的更一般性的结论。

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。