查询词典 density matrix

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。

Noll. From the irradiance distribution in two defocal planes, one in front of focal plane and the other behind, with a given detector array the elements of response matrix for each normalized term of Zernike polynomials can be obtained. For an incoming atmospheric disturbed random wavefront, with its irradiance distribution detected in two defocal planes and the response matrix, it is easy to solve the corresponding Zernike term coefficients of incoming wavefront and reconstruct the detected one.

Noll建议的Zernike多项式表征经大气扰动的入瞳处的光学波前畸变；求出由两个离焦面上的光强分布决定的归一化Zernike项在特定形状的探测器上的响应矩阵；由响应矩阵和入瞳处的波前在两个离焦面上的光强分布，求出其Zernike项的系数，从而实现波前的探测和重构。

Matrix and matrix non -singular non - degenerate mean?

矩阵非奇异和矩阵非退化是什么意思？

Firstly, we give a necessary and sufficient condition for a nonnegative square matrix to be decomposed into a product of a finite number of irreducible nonnegative matrices in chapter 1. We prove it by using Frobenius normal form in combinational matrix theory and associated directed graph in graph theory. In addition, we can limit the number of factors to three, and construct every factor.

首先，在第一章中，我们给出了一个非负矩阵可以分解成有限多个不可约非负阵的乘积的充要条件，证明过程利用了组合矩阵论中的Frobenius标准型和图论中的伴随有向图，并且将乘积中的因子个数限制到三个，具体地构造出了分解式中的每个不可约非负阵。

According to theoretical analysis, it is convergent and has good convergence if the coefficient matrix is a nonsingular matrix. Moreover, examples have been implemented on HP rx2600 cluster, and the data verify that the numerical results of this algorithm coincide with its theoretics.

在理论上，算法只要系数矩阵A是非奇异矩阵就能够收敛，而且有较好的并行性，在HPrx2600集群上进行数值试验，验证了算法的计算结果与理论相一致。

A dynamic model was developed with kinematic differential equation derived for a dual-disc over-hung rotor system with rub-impact fault. The stability of the system and stability regions were studied by setting up nonsingular linear transform matrix and by use of Jacobi matrix in combination with the theory of Routh Hurwitz. Then, the effects on the stability regions of the system were discussed with relevant parameters.

建立了悬臂双盘碰摩转子系统的动力学模型和运动微分方程，通过创建该系统的非奇异线性变换矩阵并利用变换矩阵的Jacobi矩阵结合Routh Hurwitz理论，研究了悬臂双盘碰摩转子系统的稳定性和稳定区域，并进行了相应的参数讨论。

We not only give a new Jordan canonical form J under consimilarity, but also give a practical method finding the Jordan canonical form J, and for any square complex matrix A, we also give a method finging a nonsingular matrix S such that 〓.

不但从理论上给出复矩阵的一个新的若当标准形，而且还给出了相应复矩阵若当标准形的计算方法。进一步地，我们不但给出求一个复矩阵A的合若当标准形J的简单方法，而且还给出一种求相应合相似可逆矩阵S的算法。

Let A be a nonsingular nth-order real matrix, then cond_p =||A||_p||A~(-1)||_p =1(p= 1,∞), if and only if A = cpσ, where c is a positive constant, p is a permutation matrix, or is a diagonal mat...

设A为n阶非异实矩阵，则矩阵A的求逆p-范数条件数等于1的充要条件为A=cpσ，其中c为正常数，σ是置换阵，其对角元都等于+1或-1。

This paper reviews characteristics of nonskid coatings for aircraft carrier deck s, focuses on the application situations, existing problems and development directions of resin matrix nonskid coatings and metal, matrix nonskid coatings for aircraft carrier deck s.

综述了国外舰载飞机甲板用防滑涂层的特点，着重介绍了树脂基防滑涂层和金属基防滑涂层在国外舰载飞机甲板上的应用情况、存在的问题以及未来的发展方

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

The witness also told the jury at the Royal Courts of Justice in London that he saw a paparazzo fighting with a member of the public who was trying to stop him taking pictures in the minutes before the emergency services arrived.

他还告诉在伦敦皇家法庭的陪审团，在急救服务到来之前，他当时看见一个狗仔队正和一群阻止他拍照的人打架。

The entire N／C program on a tape is made up of an accumulation of these successive data blocks.

纸带上的整个数控程序由这些连续数据单元连接而成。