查询词典 paper matrix

It is not easy to solve the problem of tensor product multilinear mapping if only matrix algebra knowledge is used. The introduction of structure matrix will make this problem much easier to be solved and more acceptable among people.

在解决张量积多重线性映射问题时，只用矩阵代数知识解决问题有些繁琐，而引入结构矩阵来解决张量积多重线性映射问题，不仅能使问题变得更加简单而且更加容易理解接受。

So with the adjacency matrix that has n vertices of a directed graph n2 units needed to store the adjacency matrix; on n vertices have an undirected graph Zexu into upper triangle, and only ...

因此用邻接矩阵来表示一个具有n个顶点的有向图时需要n2个单位来存储邻接矩阵；对有n个顶点的无向图则需存入上三角形，故只。。。

Some sufficient and necessary conditions of the full symmetric real matrix is full definite matrix are discussed.

讨论了全对称实矩阵是全正定矩阵的几个充分必要条件。

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。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。