对角地

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。

Tridiagonal block matrix elemination and sweep algorithm is successfully applied to solve the large matrix involved; central difference method is supplemented to Houbolt method to form a time integration method with estimation and correction, to solve the time integration of second order implicit non-linear equation; simplification of system equation by decoupling between the physical coordinates x and y further improves the calculation accuracy and speed.

其中：成功地引入块三对角矩阵追赶法求解上述问题构成的大型矩阵；提出中心差分法+Houbolt法的预估计—校正时间积分法，以解决二阶隐式非线性方程的时间积分问题；系统方程在物理坐标x和y上的"解耦"简化，使计算速度和计算精度得以进一步的提高。

Let R be an arbitrary commutative ring with identity, gl the general linear lie algebra over R consisting of all n × n matricesover R and with the bracket operation = xy -yx, t the lie subalgebraof gl consisting of all n×n upper triangular (resp., strictly upper triangular ) matrices over R and d the lie subalgebra of gl consisting of all n×n diagonal matrices over R.

在第三章中，对R是交换环的情形，讨论了典型李代数的导子代数的结构问题：设R是一个含幺交换环，gl是R上一般线性李代数。t是gl的所有n阶上三角矩阵(相应地，严格上三角矩阵)构成的子代数，d是gl的所有n阶对角阵构成的李代数。

In view of the usual vertical-horizontal elastic mesh's shortage in left falling stroke and right falling stroke, we present a new elastic mesh structure method—diagonal elastic mesh, which is composed of diagonal beelines of and , and divides the Chinese character image into many diamonds.

针对通常的纵横弹性网格对汉字"撇、捺"笔画特征提取的不足，提出一种新的网格构造技术——对角弹性网格，它由45°和135°的对角直线构成，将汉字图像划分为多个菱形，能够很好地适应汉字在"撇、捺"方向的变化。

Moreover, when the normalized damping matrix is diagonally dominant, it is strictly shown that decoupling the modal equations by neglecting the off-diagonal elements indeed minimizes the error upper bound.

同时，还严格地证明了，当正则化的模态阻尼矩阵是对角占优时，由忽略其非对角线元素使模态方程解耦的方法所引起的误差的上限的确能达到最小。

It is proved by the analytical and numerical method that the modulus of the Z transform of a finite impulse response sequence has no extreme values at poles (with maximums along imaginary axis and no extreme values along real axis), and the negative second order derivative of the modulus normalized along frequency axis with respect to angular frequency has maximums at the poles.

根据实测瞬态电磁脉冲响应，较好地反演了导体球和导体长椭球的冲激响应，测得了它们的雷达截面和谐振频率。用解析与数值相结合的方法证明了有限冲激响应序列Z变换的模在极点无极值（沿虚轴有极大值，沿实轴无极值），而沿频率轴的归一化值对角频率的负二阶导数在极点有极大值。

The following statements are proved:. A is equivalent to a diagonal matrix if and only if A is similar to a diagonal matrix.. If R is an APT ring, then A can be uniquely diagonalized as diag{e1,..., en} and ei divides ei+1.. R is an APT ring if and only if R/I is an APT ring, where I is a nilpotent ideal of R.

本文证明了以下结果：A相抵于一对角阵当且仅当A相似于一对角阵；若R是一APT环，则A在相似变换之下可唯一地化为对角形diag{e1，…，en｝，这里ei整除ei+1；R是APT环当且仅当R/I是APT环，这里I是环R的一幂零理想。

Then, the relation between vibration and sound, the acoustic holography method, the indeterminacy and identifiability of BSS, the BSS algorithm are discussed in detail. Based on above researches, the dissertation is divided in following four sections. The first section investigates the BSS algorithm suitable to acoustic feature separation. The algorithm of the joint approximate diagonalization of eigen-matrices is proposed. The spectra or the time-frequency distributions of source signals are the interesting features in ABD and they are separated from mixing signals by JADE algorithm. Then, the convolutive mixing model is transformed into a high-dimension instantaneous mixing model, and the deconvolution of source signals is achieved by the joint approximate block diagonalization of eigen-matrices. The proposed algorithm has a global minimum, and it is unsensitive to noise interference.

论文首先概述国内外声学诊断研究进展与盲分离研究进展，给出机器噪声声场与盲分离的数学描述，讨论了声振辐射、声全息、盲分离模型、盲分离可解性、盲分离结果不确定性、分离算法等基本问题，在此基础上，论文的研究工作分为以下四个部分：第一部分研究适用于声学特征分离的盲分离算法，提出基于特征提取的联合近似对角化盲分离算法，该算法以频谱特征或时频特征作为分离目标，从混合信号中分离源信号频谱特征或时频特征，最大限度地保留了与声学特征提取有关的频谱特征或时频特征，采用模型变换把卷积混合模型变换为一个高维瞬时混合模型，通过联合近似分块对角化算法实现源信号频谱特征与时频特征的盲反卷积。

In view of the usual vertical-horizontal elastic mesh's shortage in left falling stroke and right falling stroke, we present a new elastic mesh structure method—diagonal elastic mesh, which is composed of diagonal beelines of and , and divides the Chinese character image into many diamonds.

针对通常的纵横弹性网格对汉字&撇、捺&笔画特征提取的不足，提出一种新的网格构造技术——对角弹性网格，它由45°和135°的对角直线构成，将汉字图像划分为多个菱形，能够很好地适应汉字在&撇、捺&方向的变化。

Remember, any tile that's meant to be walked on can also act as the back splash and any cheap, square 4 x 4 tile can be installed diagonally on a backsplash.

记住，被认为走可能也作为后面飞溅和任何便宜的所有瓦片，摆正瓦片在backsplash可以被安装对角地的4 x 4。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。