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On the ground that the covariance between the disturbing gravity field elements is not isotropic, the covariance matrix has a complicated structure (its submatrix being not repetitive Toeplitz matrix) and thus its degree cannot be degraded with transformation matrix method, so it cannot be put into practice. So far, the application of least squares collocation to the modeling and data processing of the horizontal disturbing gravity field observations has not been found in literature.

由于水平扰动场元之间的协方差并非各向同性，导致协方差矩阵结构复杂(子矩阵不是 Toeplitz 循环阵)，不能利用变换矩阵将其降阶，无法付诸实践，迄今尚无最小二乘配置理论应用于水平扰动场元观测量的模型化公式和数据处理方法。

However in studying the transpose of matrix much focus has been given on the definition of symmetric matrix and anti-symmetric matrix while their properties have not been fully explored.

在高等代数中矩阵是研究问题很重要的工具，在讨论矩阵转置时给出了对称矩阵和反对称矩阵的定义，但对它们的性质研究很少。

The algorithms of MUSIC and ESPRIT are introduced, which are the most important algorithms in array signal processing. A method is proposed to make the estimation of the covariance matrix become Toeplitz matrix using the Toeplitz characteristic of covariance matrix.

第2章建立了阵列信号的模型，主要分析了两种无方向模糊的阵列：阵元数大于6的均匀圆阵和非均匀L形线性阵列，并讨论了非均匀L形线性阵列无模糊设计的方法；然后介绍了在阵列信号处理中，两种最主要的算法：MUSIC算法和ESPRIT算法。

The second method is to structure a toeplitz matrix to approach the toeplitzed signal subspace under the rule of mimimum power of noise, when the algorithm is converged, the structured toeplitz matrix is a full rank matrix, the angle information of target are all reserved and the influence of noise is minimum at this time.

第二种改进的方法是在噪声功率最小约束准则下构造一个Toeplitz矩阵，去逼近Toeplitz化后的信号子空间，当算法收敛时，所构造的Toeplitz矩阵是一个满秩矩阵，它既无损的保留了信源的角度信息又使噪声对DOA估计的影响最小。

After studying this phenomenon, the author finds that, the covariance matrix of the complex expressions of horizontal gradients of the disturbing gravity field elements has a structure of blockwise repetitive Toeplitz matrix, though the covariance within the disturbing gravity field elements is still anisotropic. Therefore, the collocation problem of the complex combination of horizontal components is similar to that of gravity anomaly, which makes the degradation be able to be completed by FFT transformation matrix.

作者研究发现，利用水平梯度的复组合，即复数表示后，扰动重力场元复组合之间的协方差函数尽管还是各向异性，但它们对应的协方差矩阵却具有分块 Toeplitz 循环阵的结构，因而水平分量复组合的配置问题与重力异常的配置问题相似，可以利用傅立叶变换矩阵进行降阶处理。

Matrix object that is the matrix transpose of the matrix.

对象，该对象是此矩阵的转置矩阵。

the fast transposition algorithm to sparse matrix expressed by triple list is introduced.this algorithm needs to determine the position in the transposed matrix position of the first element which is not equal to zero in the original matrix each row,it uses two arrays as auxiliary space.in order to reduce the auxiliary space which the algorithm needed,an improvement is made through introducing two simple variables.the improved algorithm saves a half auxiliary space compared to the original algorithm at the same time complexity.

摘 要：介绍基于三元组表表示的稀疏矩阵的快速转置算法，此算法在转置前需要先确定原矩阵中各列第一个非零元在转置矩阵中的位置，在此使用2个数组作为辅助空间，为了减少算法所需的辅助空间，通过引入2个简单变量提出一种改进算法。该改进算法在时间复杂度保持不变的情况下，空间复杂度比原算法节省一半。

To one quaternion matrix, according to its normal form, into which a quaternion matrix is transformed after decomposed, the types of decomposition of a quaternion matrix are divided into three large classes: diagonalized decomposition, triangular decomposition and triangular-diagonalized decomposition.

对单个四元数矩阵，以分解后的四元数矩阵的标准型作为分类的标准，将四元数矩阵的分解分为三大类：对角化分解、三角化分解、三角一对角化分解。

The Bidiagonal matrix method for the simulation of distillation and catalytic distillation is developed. The bidiagonal matrix method is proved to be better in convergcnce and stability by compared with the tridiagonal matrix method.

在多组分精馏塔的稳态模拟计算中，三对角矩阵法具有占用计算机内存少，无需计算偏导数矩阵等优点，但对强非理想性体系有时计算不收敛。

A set of mathematical expressions are derived including geometrical matrix,stress matrix,stiffness matrix of weak plane element,equation of equivalent nodol load caused by unit initial stress in element.

文中推导了弱面单位的几何矩阵~6，应力矩阵~6，刚度矩阵~6以及单元初应力引起的等效结点荷载{P}等计算公式。它们有别于一般文献所列算式。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。