矩阵的矩阵

By using matrix norm, matrix singular value, non-negative matrix theory, the regions of numaerical range and spectum of operator polynomial and the regularity of operator linear pencil are obtained.

8应用矩阵范数理论、矩阵的奇异值理论、非负矩阵的理论、友矩阵、算子的谱理论为工具，获得了算子多项式数值域具有的特性及其包含范围，算子多项式数值域与n-次数值域的关系，最后研究了算子线性束正则性的等价条件及谱分布情况。

In chapter three, in order to distinct N 0?matrices that defined by deferent references, we will use the following notions. A matrix is called N_0~2-matrix if the matrix is nonpositive and its all-principal minors are nonpositive.

不可约矩阵Perron余的Perron向量同原矩阵Perron向量有着继承性，另外非负矩阵的Perron余也可用于Perron根的估计，因此非负矩阵的Perron余的研究有着重要的理论价值。

We not only give a new Jordan canonical form J under consimilarity, but also give a practical method finding the Jordan canonical form J, and for any square complex matrix A, we also give a method finging a nonsingular matrix S such that 〓.

不但从理论上给出复矩阵的一个新的若当标准形，而且还给出了相应复矩阵若当标准形的计算方法。进一步地，我们不但给出求一个复矩阵A的合若当标准形J的简单方法，而且还给出一种求相应合相似可逆矩阵S的算法。

And three main steps of all subspace algorithms are explored. First, using an LQ-decomposition, the projection of the row space of specific data Hankel matrices is calculated. Next, the SV-decomposition of the projection is calculated to directly lead to the observability matrices and a Kalman filter estimation of the state sequences.

概括了子空间辨识算法的三个主要运算步骤：首先由LQ分解计算特定Hankel矩阵的行空间投影；再对该投影进行SVD，获取系统的可观测矩阵及状态序列的Kalman滤波器估计；最后由可观测矩阵和／或估计的状态序列确定系统矩阵。

And three main steps of all subspace algorithms are explored. First, using an LQ-decomposition, the projection of the row space of specific data Hankel matrices is calculated. Next, the SV-decomposition of the projection is calculated to directly lead to the observability matrices and a Kalman filter estimation of the state sequences. Last, the system matrices are extracted from the observability matrices and/or the estimated state sequences.

概括了子空间辨识算法的三个主要运算步骤：首先由LQ分解计算特定Hankel矩阵的行空间投影；再对该投影进行SVD，获取系统的可观测矩阵及状态序列的Kalman滤波器估计；最后由可观测矩阵和／或估计的状态序列确定系统矩阵。

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。

In many practice problems such as to know the resonnance frequency of a structure and to know the critical value for the stability of a dynamical system,often need to compute the eigenvalues of a symmetric matrix. The chief method to compute the eigenvalues of a symmetric matrix is first to transformate the matrix to a symmetric tridiagonal matrix similarly and orthogonally, then to use the QR method with shift to the symmetric tridiagonal matrix.

很多实际问题，如求结构振动的固有频率，动力系统稳定性的临界值等常常归结为计算对称矩阵的特征值，而首选的计算方法是先把该矩阵正交相似变换成一个对称三对角矩阵，再对这个对称三对角矩阵用带位移的QR方法。1968年J.H。

By using the methods of real representation of complex matrices, companion vector and company vector, we study and solve the problems of Jordan canonical forms, triangular and generalized diagonalization for matrices under consimilarity.

我们通过复矩阵的实表示、友向量和伴向量方法，研究并解决了合相似意义下矩阵的若当标准形、合相似意义下矩阵的三角化和矩阵的广义对角化的问题。

Therefore,a fast algorithm of NMF is presented.By some algebra formulation,the matrix to be factorized is changed into a low-dimension matrix which is a diagonal matrix whose dimension is related to the number of samples.Moreover the feature extraction for one sample only needs to calculate the inner product.

该算法通过代数变换，把对原高维矩阵的非负分解转换成非负的低维矩阵的非负分解，其求解过程只需要对一个阶数等于样本数的对角矩阵进行非负矩阵分解，同时提取某样本特征时只需要计算该样本与所有训练样本的内积。

By using properties of scalar matrices over semirings,we generalize algebraic properties for the automorphisms of matrix algebras over commutative rings and obtain some algebraic properties for the automorphisms of matrix algebras over commutative semirings.

在这一章中，我们首先利用半环上常量矩阵的性质把环上矩阵代数的性质拓广到半环上，获得了交换半环上矩阵代数自同构的一些代数性质，接下来采用积和式的方法证明任意非负交换半环上n阶矩阵代数Tn的自同构的n次幂必为内自同构。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。