矩阵的秩

This paper researches linear maps preserving orthogonality,obtains the linear maps preserving othrogonality,it is either a rank -declining or rank -keeping map or a map with nilpotent element in its codomain.

利用分块成向量的方法证明了MnMn(F为域F上所有n×n矩阵构成的乘法半群上的n×n拟正交矩阵组至多含有n个矩阵，利用方程组的解的理论证明了Mn中与给定矩阵A构成两两拟正交矩阵组的矩阵个数不超过n-Rank+1，从而得到Mn上保持拟正交性的线性映射φ要么是降秩的或者保秩的映射，要么φ的值域中含有幂零元。

The uniqueness of parameter identification is guaranteed by the full column rank of the coefficient matrix of the linear equations.

参数的唯一可辨识性由线性方程组系数矩阵的列满秩保证。

An modified BFGS algorithm to solve the unconstrained optimization, whose Hessian matrix of the minimum point of the convex function is rank one defect, is presented in this paper.

本文对凸函数在极值点的Hessian矩阵是秩亏一的情况下，给出了一类求解无约束优化问题的修正BFGS算法。

An modified BFGS algorithm o solve the unconstrained optimization, whose Hessian matrix of the minimum point of the convex function is rank one defect, is presented in this paper.

本文对凸函数在极值点的Hessian矩阵是秩亏一的情况下，给出了一类求解无约束优化问题的修正BFGS算法。

We use Hodges-Lehmann statistic to do significance test for those factors. The multiplication model is applied in the quantitative analysis and weighted least squares method is introduced to solve the multiplication model. Although the matrix of coefficients is not of full rank and the solutions of the multiplication model are not unique, we prove that all those solutions are equivalent in some sense.

本文用Hodges-Lehmann统计量对风险因子作显著性检验，将乘法模型用于数据修匀和风险因子的定量分析中，并提出了用加权最小二乘法求解风险因子的风险度量，在系数矩阵不满秩、解不唯一的情况下证明了所有解在某种意义下的等价性。

This paper concerns the construction of a low rank matrix with Hankel structure that is nearest to a given matrix.

本文研究一个给定矩阵的低秩Hankel最佳逼近及其加权逼近的问题。

The test points of it are dispersed on the surfaces of two spheres with same centre and different radius,so it solves the problem of rank decreasing of information matrix. It also has such advantages as fewe...

该计划在两个不同半径的同心球面上布测试点，解决了信息矩阵的降秩问题，具有试验点数少、实现方便和模型估计精度高的优点，在理论上和实际应用中均具有一定价值。

The relationship between total species and the theoretical rank of the two-dimensional matrix was deduced and it was found that the rank of data matrix was smaller than the total species in sample.

推导了型体总数与两维矩阵的有效秩之间的关系。

For solving the singular linear equations,we present the iterative methods based on proper splittings and give the convergence analysis.

在奇异线性方程组的求解方法中，我们提出了基于正则分裂的二级迭代法并给出收敛分析；在论文的第三章我们对奇异的结构化矩阵的置换秩进行了研究，得到了一些结论并给出了应用。

In chapter two, we first consider the linear system WAWx=b, where A is an m*n rank-deficient matrix. Then we consider the weighted Frobenius norm on data, and get the formula of W-weighted Drazin inverse solution of the linear system.

第二章的前半部分介绍了线性系统 WAWx=b 的加 W 权的 Drazin 逆解在范数带参数的 Frobenius 范数意义下的条件数，这里矩阵 A 为一个 m*n 的秩亏阵。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。