相似变换

The red and black ordering method about the coefficient matrix of a class of linear equations and the condition number of schur complement matrix deduced from red and black matrix are studied.

利用矩阵相似变换推导出红黑排序矩阵中的舒尔补的特征值和条件数表达式。

The pupose of the research is to develops public key encryption and digital signature shemes based on matrix canonical decomposition problem, or matrix diagonalization problem over Z/n, the ring of integers with modulo-n addition and multiplication in particular, where n is an RSA modulus.

本课题研究基于矩阵经典分解问题，特别是Z/n上矩阵对角化问题的公钥密码与数字签名算法，其中n是一个RSA模数。新算法采用由一个矩阵多项式构成的多维单向陷门函数，其单向性由矩阵对角分解问题(即通过相似变换将矩阵化为对角型的问题)的复杂性来保障，对该函数求逆的陷门由矩阵的特征值或特征向量提供。

Then the methods for solving the characteristic polynomial and the eigenvalues of square matrices using similar transactions are showed, and several examples are given.

然后指出了利用相似变换在求方阵的特征多项式以及特征值时的方法，并列举若干实例给予了说明。

WGS-84 geodetic latitude and longitude from GPS was projected by similarity transformation method, and they were transformed coercively to realize coordinate matching.

并用相似变换法将GPS接收到的WGS-84大地经纬度高斯投影后强制转换统一，以实现坐标匹配。

Ngai and Wang [9] introduced the notion of finite type and described a scheme for computation of the Hausdorff, Box dimension when the finite type occurs, which, however, forces the ratios to be exponentially commensurable.

Ngai和Wang[9]提出了有限型的定义并给出了当迭代函数系统是有限型时计算系统吸引子Hausdorff，Box维数的方法，但有限型的定义要求相似变换的压缩比必须满足对数值可公度。

So the conformal transformation model for the image rectification is taken as a beginning to deduce the relation between the accuracy of an arbitrary point and the accuracy of control points, besides, according to such relation, the inverse distance power method is used to give the spatial interpolation for the image rectification accuracy, which also achieved the interpolation value in x or y directions.

并以相似变换作为影像纠正的基本模型，推导了纠正后任意点精度与控制点精度的关系，基於此选择采用空间插值方法，插值影像纠正后任意点不同方向上的点位的精度。

The main difficulties in the study of the dimension of the intersection lie in that the number of similitudes used in the construction may vary from step to step.

研究这一类交集维数的难点主要在于每一层迭代中相似变换的个数总是变化的。

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。

Based on the 2 sets of CPI-accuracy plane coordinates composed by the 14 GPS control points along the Hunan-Guangxi railroad line, we carried out coordinate transformation using the Similarity Transformation Method and the Affine Transformation Method in different common point numbers and position distributions.

以湘桂线14个GPS测量点的两套CPI精度的控制点平面坐标为依据，分别用相似变换、仿射变换及不同公共点个数求转换参数进行坐标转换，分析成果精度之间的差异及规律。

The characteristic vector of the real symmetric matrix should be found out, which is orthogonalized and normalized to a standard orthogonal base and is used as row vector to construct the transformation matrix P, so the P~(-1)AP can be made into diagonal matrix.

实对称矩阵A经相似变换P-1AP可化为对角矩阵，在x =Py 下，不一定能化A的二次型为标准型；应寻求对称矩阵A的特征向量，将其正交化并单位化作为标准正交基，作为列向量构造变换矩阵P，可使P-1AP=Λ为对角阵，在x =Py 下，要将二次型化为标准型，且二次项系数即为对角阵Λ主对角线上元素。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失