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Then the matrix Having these solution vectors as its column vectors is called a fundamental matrix for the system in Fundamental Matrix Solution Because the column vector .

则以这些解向量为列的矩阵被称为这个系统的基本矩阵。

In this paper, firstly the elimination tree theory is introduced in brief, and the structure of Jacobian matrix is determined by use of symbolic factorization; then by use of sparse vector method each column of lower triangular matrix L and each row of upper triangular matrix U are solved.

介绍了消去树理论，并采用符号因子分解技术确定雅可比矩阵的结构，然后采用稀疏向量法求取L阵的每行和U阵的每列。

This thesis has mainly contributed two results in theory: one is that the covariance matrix is not positive definitive if the number of sampling is least than the number of variables, the other is that the covariance matrix of discrete sample is positive definitive if and only if the sum of every random column vector of data matrix is non I-linear combination.

本论文在理论上，主要得出两个新的结果：ⅰ抽样调查中，若样本的个数少于变量的个数则样本协方差矩阵恒为非正定；ⅱ离散型样本协方差矩阵正定的充要条件是样本资料阵的各随机列向量是非I-线性组合。

Maximum model values are found for the channel matrix Hi of each user and for each column vector of the matrix, position information of the matrix is transmitted to a transmitting terminal, the transmitting terminal reconstructs the amplitude of each element of the column vector after receiving the position information, and phase position is quantized, wherein, after reconstruction, the amplitude of the element with the maximum model value is larger than that of other elements of the column vector, and a quantized angle of the element with the maximum model value is smaller than that of the other elements of the column vector; c.

对每个用户的信道矩阵Hi，对该矩阵的每个列向量，找出其最大模值，将其位置信息发送给发射端，发射端收到后对该列向量各元素的幅度进行重构，相位进行量化，其中最大模值的元素重构后其幅度大于该列向量其余元素的幅度，其量化角度小于该列向量其余元素的量化角度；c。

In this scheme, channel matrix is combined with encoding matrix to form new decoding matrix.

二、将TR-STBC编码技术与OFDM技术结合起来，提出了2种新的MIMO-OFDM系统方案。

Several important matrix function such as e〓, log (1+A), cos (1+A) and A〓 are approximated via truncated matrix continued fractions, and the error bounds associated with the continued fraction approximants of these matrix function are given.

在第六章，我们研究了矩阵函数的数值计算，我们给出了几个比较重要的矩阵函数如e〓，log（1+A），cos与A〓的连分式逼近算法，并给出了各自的误差分析。

In this paper, taking the downward continuation of potential field as an inverse problem of upward continuation, we obtain a convolution type linear integral equation for downward continuation. Making use of the orthogonal symmetry characteristic of Fourier transform matrix, and combining the principles of singular value decomposition of matrix and generalized inverse, we proposed a stable generalized inverse method for downward continuation of potential field, called wavenumber domain generalized inverse algorithm, which doesn't need the computation for inverse matrix. It resolves the instability of potential field downward continuation of large depth.

本文通过把位场向下延拓视为向上延拓的反问题，得到向下延拓的褶积型线性积分方程，再利用Fourier变换矩阵的正交对称特性，并结合矩阵的奇异值分解和广义逆原理，提出了一种稳定的不需要进行求逆运算的位场向下延拓广义逆方法——波数域广义逆算法，解决了位场大深度向下延拓的不稳定性问题。

On the basis of the conclusion above, the nonlinear weak controllable vectors can be obtained, which compose the second class of weak controllable matrix, by means of matrix transfermations of the first class of weak controllable matrix. Furthmore the second criterion of weak controllability, accessibility and strong accessibility, which is more standard, more succinct and more practical, is obtained. On the basis of the first criterion and the second criterion, several important problems about nonlinear controllability are discussed, which include 1 local controllability; 2 three classes of local controllable decomposition, separately by means of local coordinate changes in the neighborhood of a nonsingular point, a point on a singular surface or a designated point x〓 with a designated input u〓; 3 the character of controllability of the ith state variable x〓 in different controllable areas and their boundaries.

在第一判别定理和第二判别定理的基础上，我们分析了非线性系统受控性质中的几个重要问题，所得到的结论包括i得到了非线性系统在可平衡点附近的能控性判别定理；ii分别给出了非线性系统在非奇异点、s阶奇面以及在状态空间内给定的一点x〓和输入u〓上的三种状态分解形式以及相应的求解方法；利用系统的Ⅰ型弱能控矩阵与Ⅱ型弱能控矩阵秩相等的条件，得到了只用系统的前n个弱能控向量来判断系统的弱能控性的判别定理；iii通过引入系统状态分量的三类受控区域边界的定义及相应的求解方法，初步探讨了非线性系统各个状态分量在不同的受控区域及其边界上的受控性质。

Meanwhile, in order to fix defect of former methods, an optimal source array weight matrix is presented to estimate Green's function matrix by analyzing the estimation covariance of Green's function matrix.

同时指出了现有方法存在的不足，并在此基础上通过研究格林函数矩阵的估计协方差，提出了一种最佳估计算法。

CvEM::COV_MAT_DIAGONAL - a covariation matrix of each mixture may be arbitrary diagonal matrix with positive diagonal elements, that is, non-diagonal elements are forced to be 0's, so the number of free parameters is d for each matrix.

每一个混合的协变矩阵都是任意的正对角阵，也就是说，非对角位置的值必须是0，因此每一个矩阵的自由参数为d。

I was up all night because I was in pain, she said.

我整夜，因为我在疼痛，她说。

A crow caws /craoks.

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