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In this paper, an algorithm for finding the inverse matrix of tridiagonal matrix by sloving systems of linear algebraic equations is proposed.

根据三对角矩阵的特点,给出一种利用解线性方程组的方法求三对角矩阵的逆矩阵的算法。

An orthogonal matrix is an invertible matrix for which the inverse is equal to the transpose.

正交矩阵是可逆矩阵,其逆矩阵等于其转置矩阵。

Compared with the other image projection analysis methods, the proposed method has the following properties:( 1 ) the scattering matrices are directly based on image matrices;(2) the efficient projection vectors are statistically uncorrelated;(3) the within scattering matrix is not necessarily invertible and some matrix inversions are not performed.

在ORL标准人脸库和NUST603人脸库上的试验结果表明,上述图像投影鉴别分析方法在识别性能上较以往的方法有一定的提高,尤其是特征抽取的速度有明显的提高。

Secondly, we discuss some properties of matrix above which are similiar to the irreducible nonnegative matrix.

其次,讨论了上述矩阵中类似于不可约非负矩阵的一些性质。

Particularly, the weight configuration matrix is not necessarily symmetric or irreducible, and the inner-coupling matrix need not be symmetric.

特别地,文中的构形矩阵不必要是对称或不可约阵,内部耦合阵也不必为对称阵。

The main contributions of the thesis are as follows: Using invariants and matrix theory, especially the special properties of eigenvalues and eigenvectors of the so called irreducible matrix, we put forward several effective new algorithms for the complete matching problem under Euclidean transformation, similarity transformation and general affine transformation.

论文的主要贡献如下:利用不变量和矩阵理论,特别是巧妙地利用了不可约矩阵的特征值和特征向量的特殊性质,提出了求解欧氏变换、相似变换和一般仿射变换下完全匹配情形的点模式匹配问题的几种非常有效的新算法。

For different polynomials g, if the characteristic polynomial of a n matrix A is irreducible, then we get some theorems to determine matrix equations g =A solvable; if it is reducible, then, to see n-dimension space vectors M over a field F as F-module, we use module theory to determine these equations solvable such that it is simpler and clearer to investigate these questions.

对于不同多项式g,当n阶矩阵A的特征多项式为不可约的,我们给出了矩阵方程g=A有解的判定定理;当A的特征多项式为可约的,把域F上的n维线性空间M作为由A导出的F -模,我们利用模论知识来决定矩阵方程g=A有解性,从而使这一问题变了简单,研究思路更加清晰。

The asymptotic synchronization in a lattice of x-coupled nonidentical Lorenz equations is considered, the external coupling matrix is an n×n irreducible symmetric real matrix having zero row sums and nonpositive off-diagonal elements.

考虑外部耦合格式为n×n阶实对称不可约,行和为零且对角线以外的元素非正的矩阵,内部耦合格式为仅有x-分量参与耦合的非恒同Lorenz格点系统的渐近同步。

Using the Mindlin theory, the four-node finite element shell modal of healthy and damaged structure is formed; Using Green Function theory, the fluid around the structure is considered to be inviscid, irrotational and incompressible, and then the effect of fluid to structure is translated to the added mass matrix compared with global mass matrix using BEM.

基于Mindlin理论,本文建立了描述健康和损伤的四结点有限元板壳单元模型;基于Green函数理论,将结构所处的流体环境考虑为无粘、无旋、不可压缩的理想流体,推导了三维问题拉普拉斯方程的基本解,并利用边界元方法将流体对结构的影响归结为对结构整体质量矩阵的影响;针对各向同性损伤单元,采取刚度各向整体弱化的方法分析;对于各向异性损伤单元,采用Kachanov理论,引入了x和y两个方向的弹性损伤折减系数。

The relationship between 8 isometry transforms matrix and its corresponding invert matrix was given and the calculation of fractal codes was simplified.

此外,还给出了8种旋转变换矩阵与其对应逆矩阵的关系,从而进一步简化分形码求解。

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