查询词典 diagonalizable matrix

In this paper, the inertial theorem of real symmetric matrix has been proved by three methods in three aspects: the relationship between real symmetric matrix and real quadratic form, the relationship between real symmetric matrix and symmetric bilinear function of real linear space.

从实对称矩阵与实二次型的联系、实对称矩阵与实线性空间的对称双线性函数的联系以及将实对称矩阵作为研究主体这三个角度，介绍实对称矩阵的惯性定理的三种证明，以期加深对实对称矩阵的惯性定理的理解。

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 method of estimation in paper [7] is to build fitness function by the 2-norm of error matrix directly. For the error matrix is a Toeplitz matrix, a novel fitness function was presented. Then a new method, the real-valued genetic algorithm which is based on genes weights variation independently, is developed in this paper.

文献[7]提出的估计方法直接以误差矩阵的2范数建立适应度函数，文中利用该矩阵是Toeplitz矩阵的特性，构造了一个新的适应度函数，提出了一种基于基因分量独立变异的实数遗传算法。

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。

In the paper, the friction coefficient of the friction pairs of Al2O3 matrix ceramic/45# steel during sliding experiments were studied, and the worn trace's micrographs of Al2O3 matrix ceramic were observed and analyzed, and the wear mechanism of Al2O3 matrix ceramic in dry friction and oil Iubrication were analyzed.

摘 要：本文对Al2O3基陶瓷材料/45#钢摩擦副的摩擦系数与45#钢/45#钢的摩擦系数作了对比滑动摩擦试验研究，观测分析了Al2O3基陶瓷材料磨痕形貌，并就干摩擦，油润滑状态下Al2O3基陶瓷材料的磨损机理进行了分析。

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。

We stopped by the old fashion ice cream parlor Manhattan Beach Creamery for some refreshment. The "No Shoes, No Shirt, No Problem" sign on the wall epitomizes the beach lifestyle.

我们去商店区的一家老式冰淇淋店坐坐，墙上挂著「没鞋，没上衣，没问题」的牌子完全捕捉了海滩生活的随性及风格。

"If therefore", argues Bellarmine we can offer our prayers and our satisfactions in behalf of those detained in purgatory, because we are members of the great body of Christ, why may not the Vicar of Christ apply to the same souls the superabundant satisfaction of Christ and his saints--of which he is the dispenser?

" "因此，如果"，认为贝拉明（德indulgentiis ，十四）"我们可以提供我们的祈祷和我们满意的代表那些被拘留在炼狱，因为我们是成员的伟大基督的奥体，为什麼可能不是牧师基督适用於同样的灵魂满意的过剩是耶稣和他的圣人-他是在配药？