矩阵的秩

This article presented a new fast algorithm of Moore-Penrose inverse for an m×n symmetric Loewner-type matrix with full column rank by forming a special block matrix and studied its inverse. Its computation complexity was O+O(n^2), but it was O(mn^2)+O(n^3) by using L(superscript +)=L(superscript TL^(-1)L.

论文通过构造特殊分块矩阵并研究其逆矩阵，给出了秩为n的m×n对称Loewner矩阵Moore-Penrose逆的快速算法，该算法的计算复杂度为O+O(n^2)，而通过L=L(上标 TL^(-1)L计算的复杂度为O(mn^2)+O(n^3)。

In this paper, for m× n Loewner-type matrix or symmetric Loewner-type matrix with full column rank, we form special block matrix firstly and research their triangular factorization or of its inverse, and then get the fast algorithm of the minimal norm least squaresolution .

本文对于秩为n的m×n阶Loewner型或对称Loewner型矩阵L，通过构造特殊分块矩阵并研究其逆的三角分解或自身三角分解，进而得到了线性方程组Lx=b的极小范数最小二乘解快速算法，计算复杂度为O+O(n~2)，而一般方法的计算复杂度为O(mn~2)+O(n~3)。

Firstly, we apply block AOR method to find the least square solution of minimal norm to the rank deficient linear systems where A is a complex m*n matrix with rank k.

首先，我们把求解线性方程组的块加速超松弛迭代法应用于求解亏秩线性方程组的最小范数最小二乘解，其中线性方程组的系数矩阵A是秩为k的m*n复矩阵。

Means of non -singular determinant is not equal to 0, the matrix must be non - degenerate square matrix is full rank is, the matrix is not necessarily ...

非奇异的意思是行列式不等于0，矩阵一定是方阵非退化是矩阵是满秩的，矩阵不一定是。。。

If A is a symmetric positive definite matrix, then the quadratic form x~ TAx can be written as a sum of squares. Equivalently, A is a sum of rank one matrices VV~T.

若A是对称正定矩阵，则二次型x~ TAx 能写成平方项的和，即A是秩为1的矩阵VV~T的和。

The second method is to structure a toeplitz matrix to approach the toeplitzed signal subspace under the rule of mimimum power of noise, when the algorithm is converged, the structured toeplitz matrix is a full rank matrix, the angle information of target are all reserved and the influence of noise is minimum at this time.

第二种改进的方法是在噪声功率最小约束准则下构造一个Toeplitz矩阵，去逼近Toeplitz化后的信号子空间，当算法收敛时，所构造的Toeplitz矩阵是一个满秩矩阵，它既无损的保留了信源的角度信息又使噪声对DOA估计的影响最小。

Under the condition of knowing zero eigenvalue algebraic multiplication ,the authors have discussed the use and necessary relationship between matrix zero eigenvalue algebraic multiplication and matrix rank.

在已知零特征值代数重数时，给出了矩阵零特征值代数重数与矩阵秩之间的内在必然联系，及其一般应用。

Using the judgment matrix of detectable and locatable of gross errors in surveying error and reliability theory, it is proved firstly that the number of zero column vectors in LZD\'s judgment matrix equals to the rank defects of LZD\'s coefficient matrix. And then, LZD\'s matching equation having the detectability and locatability of gross errors is verified by a series of tests. These conclusions powerfully support the following researches on algorithms of detecting DEM deformations in theory.

运用误差与可靠性理论中的粗差可发现和可定位判断矩阵，证明了LZD算法判断矩阵中零列向量的个数等于LZD算法系数阵列秩亏数，试验验证了LZD算法匹配方程具备粗差发现和定位能力，为DEM差异探测算法提供了理论支持。

In this paper a new method is proposed in order to suppress the coherent interference. First, utilizing the interpolate method, the real array can be virtually shifted under coherent interference, several covariance matrice are gererated after the virtual shifting. By averaging the previous results, a new covariance matrix is obtained. It is a full rank matrix.

提出一种新的相干波束形成方法，利用内插变换对相干背景下的真实阵列进行虚拟平移，得到多个虚拟平移后的信号协方差矩阵；对其进行平均后，所得到的相干信号协方差矩阵具有满秩性。

First, utilizing the interpolate method, the real array can be virtually shifted under coherent interference, several covariance matrice are gererated after the virtual shifting. By averaging the previous results, a new covariance matrix is obtained. It is a full rank matrix.

软件简介：提出一种新的相干波束形成方法，利用内插变换对相干背景下的真实阵列进行虚拟平移，得到多个虚拟平移后的信号协方差矩阵；对其进行平均后，所得到的相干信号协方差矩阵具有满秩性。

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。