查询词典 jacobian matrix

Some important applications of structure matrix in the tensor product multilinear mapping are given. Compared with the method of matrix algebra knowledge, the proposed method enjoys obvious advantages.

给出了结构矩阵在解决张量积多重线性映射问题时的一些重要应用，经过与用矩阵代数知识解决此问题相比较对照，更显示出用结构矩阵解决问题的优越性。

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。

In this paper, introduces firstly a concept of polynomial coefficient matrix, and then the polynomial multiplication is masterly changed into the computing of matrix multiplication. Then a theorem is received. Throughout the process, the steps are very clear and the calculating is pretty simple.

该文首先引进了一个多项式系数矩阵的概念，然后巧妙地将多项式的乘法转变为矩阵乘法的运算，得到了一个定理，步骤清晰，计算简单。

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。

This paper analyzes the network of the air cooling system using network matrix method, then gives the air cooling network matrix of a large-scale motor.

本文采用网络矩阵法计算电机的通风网络，并以一台大型电机为例，列出了其通风系统的网络矩阵。

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。

Researches reveal that students who suffer from corporal punishment tend to resort to violence in their future life.

研究表明遭受过肉体惩罚的孩子倾向于在他们今后的人生中使用暴力。

Total sugar of sarcocarp and chlorophyll of pericarp increased firstly, and then decreased afterward along with altitude; Titratable acidity, ascorbicacid and anthocyanin of pericarp were increased along with altitude; The content of protein increased firstly and decreased afterward along with altitude; Carotenoid of pericarp were decreased along with altitude.

果肉总糖和果皮叶绿素含量随海拔高度升高先升高后降低；可滴定酸、维生素C和果皮花青苷含量均随海拔升高而升高；蛋白质在1720m处最大，1420m处最小；果皮类胡萝卜素随海拔升高而降低。