The parity check matrix and minimum rank distance of them are given.
其中主要研究工作以及取得的研究成果包括：1。
The Jacobi matrix rank one update problems, given either their mix-type eigenpairs or their pricinpal submatrix and defective eigenpairs(the eigenvalues of the matrix and some elements of the corresponding eigenvectors) are also discussed.
n阶对称箭形矩阵与n阶Jacobi矩阵一样只有2n-1个非零元素，类似Jacobi矩阵逆特征值问题的提法，本文提出并讨论了六类对称箭形矩阵逆特征值问题，研究了这类矩阵的结构性质，得到了问题有解的充分必要条件及求解的数值算法和数值算例。
The uniqueress of identification is guaranteed by the full rank of the coefficient matrix of the utilized linear equations.
选用的线性方程组具有列满秩的系数矩阵，保证了系统参数的唯一可识别性。
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。
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。。。
Condition sufficient to allow memory conflict-free access of a template in an XOR-scheme is that its generation matrix is full rank.
异或方案能使模板的访存存储器无冲突的充要条件是模板的生成矩阵是满秩的。
Simulation results show that due to the errors the rank of the covariance matrix will increase and the SINR performance will descend.
实验结果表明：滤波器相频响应误差会使自相关矩阵的秩增加、SINR性能下降。
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。
Therefore, the principal component estimate is applied to rank defect free net adjustment, and deduce the calculation formula of inverse weight matrix of estimated parameters, as well as deduce the constraints that rank defect free net adjustment must meet with.
由此，将主成分估计推广到秩亏自由网平差中，导出求解未知参数及其协因数的公式，并据主成分估计演绎出用附有条件的参数平差法求解秩亏自由网的条件方程。
By using conclusions of matrix rank, a necessary and sufficient condition of diagonalization for square matrix is given.
本文利用矩阵秩的相关结论，给出并证明了方阵可对角化的一个充要条件。
Solving such a system would encounter some intricacies if its leading principal submatrix, i. e. the stiffness matrix, is rank deficient. This is believed to be one of the main reasons that many programmers would unwillingly give up the Lagrange multiplier method but select the penalty function method.
当其中的主子阵亏秩时，求解会遇到许多困难，这些困难往往是导致许多程序员放弃Lagrange乘子法而选择罚函数法的根本原因。
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。
Let A be a matrix of full column rank, and let x be a computed solution to the linear system ATAx = b.
设A是一个列满秩矩阵，x是线性方程组ATAx=b的一个计算解。
Using an aggregation matrix with full column rank to map the on-line optimization variable sequence into a new one, the number of on-line optimization variables is cut down without reducing the control horizon. A sufficient condition is presented to check whether the control variable sequence can be aggregated.
通过一个列满秩的集结矩阵将维数较小的控制变量序列映射成在线优化变量序列，在不缩短控制时域的情况下，降低了在线优化变量的个数。
In chapter 3, we first discuss the completely positive matrix and give a sufficient and neessary condition of whence a double nonnegative matrix is a completely positive matrix, i. e., For A = 6 DNNn and suppose that A = T^T where T is a real kxn matrix and k = rank.
第三章首先对完全正矩阵进行了讨论，得到双非负矩阵是完全正矩阵的一个充要条件，即：设A=a_(ij∈DNN_n，如果A=T~TT，那么A∈CP_n当且仅当存在m个非零向量x_1，…，x_m∈S_T~*使得下式成立：x_1x_1~T x_2x_2~T … x_mx_m~T=I_k，其中，T是k×nk=rank
First, it diagnoses and analyses the maglev train's suspension system and traction system by applying the FTA and fuzzy FTA method. Furthermore, it presents the new way to solute the diagnosis searching arithmetic by building the searching matrix based on the factors such as components'key weightiness, faults happen probability, searching cost. Then it can get optimal searching sequence for seeking the reason to the faults. Second, it builds the train's rank evaluation model based on multiple hiberarchy neural networks, after it takes the strategy that set the component diagnosis and whole train fault rank evaluation into two steps. Third, it deeply analyses reliability of the maglev train's power system with function-correlated feature, by the method that combining the FTA with the Markov model. Finally aiming at maintenance ahead of the fault, it proposes the blue print for the maglev train's maintenance. What's more, it introduces the design and realization to recorder for the train run data in detail.
应用故障树和模糊故障树分析法对磁浮列车悬浮系统、牵引系统进行全面的诊断分析，提出了以部件关键重要度、故障概率、搜索代价为因素，建立搜索决策矩阵，综合排序的搜索算法；采取部件诊断和列车集中评估相结合的分层诊断策略，建立基于多重神经网络的列车故障等级评估模型；结合故障树和马尔可夫模型对具有功能相关特性的列车电源系统进行可靠性分析；着眼事前维修，提出了列车运行维护方案，并设计实现了列车运行数据记录器。
In order to deal with the consistency problem of judgement matrix in AHP, a new method, named accelerating genetic algorithm, is presented to compute rank weights and check the consistency of judgement matrix at the same time in this paper.
为处理 AHP中判断矩阵的一致性问题，直接从判断矩阵的定义出发，提出用加速遗传算法同时计算 AHP中各要素的排序权值和检验判断矩阵一致性的新方法。
In the numeral value algebra, we can adopt matrix decomposition to solve a problem by transforming the large-scale complicated problem into small-scale simple problems; in the applied statistics, we can get the low rank approximation of the original data matrix through matrix decomposition so as to discover the data`s internal connection.
在数值代数中，利用矩阵分解可以将规模较大的复杂问题转化为小规模的简单的问题来求解；在应用统计领域，通过矩阵分解得到原数据矩阵的低秩逼近，从而发现数据的内存接头特征；在机器学习和模式
Because the rank of the augmented channel matrix is always equal to the number of transmitting antennas, the algorithm can work well in an ill-conditioned channel.
由于扩展信道矩阵的秩等于发射天线数，该算法对信道缺秩的情况不敏感。
An approach similar to spatial smoothing for array signal processing is adopted to recover full rank of convariance matrix of time delays, and the real domain approach to fasten the operation is also in the consideration. At the same time, an approach to mitigate the first time delay errors for a pair of terminal is also presented, which exploits the probability analysis. Several areas are constructed to distinct the estimations, and put the estimations of couples of samples into the distinct area, choose the area which has most estimations, get the last result through the avaraging. The simulation results show that the proposed approach provids high resolution time of arrival estimations.
本文提出了将TLS-ESPRIT算法应用于到达时间估计，并且在小样本的前提下，利用空间平滑的方法将路径的自相关矩阵恢复成满秩，同时将实值运算应用于谱估计算法，加快了运算速度；同时为了减小首径衰落的影响，本文提出了基于概率分析的首径到达时间估计方法，该方法主要选取了数个样本下的前几个估计值，通过划定一定宽度的区间，选取估计值出现频率最高的区间；将该区间中的各个估计值求平均值后，得到最后的首径到达时间估计，实验表明，该方法能够获得较小的估计误差，提高了估计精度。