矩阵的秩

For general bipartite system [34], a complete set of invariants for generic density matrices with full rank has been presented.

对于一般的两体系统，[34]中给出了满秩一般密度矩阵的不变量的完全集合。

The number of chosen transmit antennas is equal to the rank of channel matrix to ensure that the resulting channel matrix is full column rank.

为了保证信道矩阵是列满秩，因此选择出的天线子集中的发射天线数量等于信道矩阵的帙数。

Then,a new fast algorithm of the minimal norm least squares solution for linear system whose coefficients is an m×n symmetric Loewner matrix with full column rank is given by forming a special block matrix and researching the triangular factorization of its inverse.

对于工程计算中常常遇到的一类线性方程组的求解，通过构造特殊分块矩阵并研究其逆矩阵的三角分解，给出了求秩为n的m×n阶对称Loewner矩阵为系数阵的线性方程组，及极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

In Chapter three, by constructing a special partitioned matrix and studying the fast triangular factorization of its inverse matrix, we respectively give fast algorithms for the minimal norm least squares solutions of linear equations which coefficient matrices are n×m Toeplitz type matrices and Vandermonde-Loewner type matrices with full column rank.

第三章通过构造特殊分块矩阵并研究其逆矩阵的快速三角分解，分别给出了求以秩为m的n×m阶Toeplitz型矩阵和Vandermonde-Loewner型矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法，并通过算例将新算法与已有的法方程组的方法和正交化方法作了比较。

Also, the general solutions of the firing vector in the state equation of a Petri net are proposed.

这些方法都是基于网关联矩阵的满秩分解。

Based on the analysis of this matrix, the constraints for the coefficient matrix were got.

通过对该系数矩阵的分析，得到关於此矩阵的约束条件，并在此基础上，推导了判断此矩阵秩的大小的一个充分条件。

A method was reported that calculating order through establishing matrix in phase equilibrium system and compared with phase rule, the relation between order and number of independent component was found.

本文通过相平衡体系中矩阵的建立，解出其秩，与相律进行比较，找出秩与独立组分数间的关系。

Based on the special decomposition of Hankel matrix, we can transform the problem of approximating a given matrix with a positive semidefinite real Hankel matrix of lower rank to a smooth unconstrained optimization problem.

对矩阵的低秩Hankel半正定矩阵逼近，采用特殊的分解形式，可将其转化为一个无约束的优化问题进行求解，本文应用拟牛顿方法求解无约束优化问题。

In chapter 5, we investigate the iterative methods for solving the linear systems by the homotopy perturbation technique, and the numerical rank of a matrix in the matrix computations are considered, especially the ill-conditioned matrices.

本文第五章中我们首先利用同伦摄动技巧考察了线性方程组的迭代解法。其次，从数值计算的角度考察了矩阵的数值秩问题，尤其是病态矩阵。

The structured properties of tridiagonal inverse M-matrices are then studied in detail by using graph theory and combinatorial mathematics, and a sufficient condition for a nonnegative tridiagonal matrix to be an inverse M-inatrix is given.

第一部分分析证明了逆M-矩阵的结构特点和在Hadamard积下的封闭性；第二部分分析几类特殊矩阵的结构特点，以及它们逆矩阵的构造方法；第三部分研究对称不定矩阵秩一校正的Bunch-Kaufman分解和相应的算法。

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。