分块矩阵加权Moore-Penrose逆的块独立性

本文研究了分块矩阵关于加权Moore-Penrose逆的块独立性问题.利用加权Moore-Penrose逆的定义和性质,获得了2×2、1×2和2×1分块矩阵关于加权Moore-Penrose逆块独立的一些充分必要条件.     

分块矩阵g-逆的块独立性

本文研究分块矩阵g-逆的块独立性,得到两个和三个复矩阵块独立的充分 必要条件,并揭示了不同定义下的块独立性定义之间的联系.     

关于分块矩阵〔ABCD〕的g-逆的块独立性

本文证明了分块阵M=〔ABCD〕的g-逆有块独立性的充要条件是M适合秩可加性条件,M~+有一特定的表达式的充要条件也是M适合秩可加性条件.本文还给出了包含M的g-逆的子块的不变矩阵以及这些子块的定义方程.     

块Toeplitz方程组的快速块Gauss-Seidel迭代算法

本文研究块Toeplitz方程组的块Gauss-Seidel迭代算法。我们首先讨论了块三角Toeplitz矩阵的一些性质,然后给出了求解块三角Toeplitz矩阵逆的快速算法,由此而得到了求解块Toeplitz方程组的快速块Gauss-Seidel迭代算法,最后证明了当系数矩阵为对称正定和H-矩阵时该方法都收敛,数值例子验证了方法的收敛性。     

块—Cayley-Hamilton定理的应用

利用块—Cayley-Hamilton定理,得到了一类各子块是两两可换的分块阵A的广义逆AT,S(2)的表示式,并给出了计算它的块有限算法.     

长方形Toeplliz-块矩阵的快速逆Cholesky分解

该文对m×n阶长方形Toeplitz-块矩阵A，提出了一种ATA进行逆Cholesky分解的快速算法．该算法乘法运算次数只有O（mn）次．     

块复合矩阵的块特征值

本文首先讨论了块复合矩阵之块特征值的若干性质,证明了块复合矩阵的块特征值集合是完全的时侯,其相似于块对角阵的几个充要条件。进而利用张量积给出了块复合矩阵之块特征值的包含域。最后讨论了块复合矩阵之块特征值按范数的界。本文给出的主要结果分别推广及改进了文[1]-[5]中的相应结论。     

块复合矩阵的块C-特征值

本文研究了块复合矩阵的块C-特征值的问题.利用理论推导证明的方法,获得了块复合矩阵的块C-特征值,块C-特征向量的若干性质以及块复合幂等阵的块C-特征向量块线性相关的等价条件的结果,推广了文献[6]中块复合矩阵的块C-特征向量块线性无关等价表征的结果.     

无限广义块Toeplitz和Hankel矩阵求逆的统一方法

利用Sylvester位移方程的统一办法给出所谓的无限广义块Toeplitz和Hankel矩阵的求逆公式。     

某些2×2分块矩阵的群逆

令R是有1的结合环,本文中给出R上某些2×2块阵的群逆的存在性及表示.     

分块矩阵的初等变换

本文将矩阵的初等变换的概念推广到分块矩阵上并建立了计算分块矩阵的逆矩阵和分块方阵的行列式的若干简易方法．     

Algorithms for Finding the Inverses of Factor Block Circulant Matrices

In this paper,algorithms for finding the inverse of a factor block circulant matrix, a factor block retrocirculant matrix and partitioned matrix with factor block circulant blocks over the complex field are presented respectively.In addition,two algorithms for the inverse of a factor block circulant matrix over the quaternion division algebra are proposed.     

Block toeplitz products of block toeplitz matrices

Necessary and sufficient conditions for the product of two block Toeplitz matrices to be block Toeplitz are obtained. In the special case of two Toeplitz matrices, the conditions simplify considerably and, when combined with known necessary and sufficient conditions for a nonsingular Toeplitz matrix to have a Toeplitz inverse, provide a simple characterization of the additional matrix structure required by a subclass of Toeplitz matrices in order for it to be closed with respect to both inversion and multiplication.     

Block maps and Fourier analysis

We introduce block maps for subfactors and study their dynamic systems. We prove that the limit points of the dynamic system are positive multiples of biprojections and zero. For the Z_2 case, the asymptotic phenomenon of the block map coincides with that of the 2 D Ising model. The study of block maps requires a further development of our recent work on the Fourier analysis of subfactors. We generalize the notion of sum set estimates in additive combinatorics for subfactors and prove the exact inverse sum set theorem. Using this new method, we characterize the extremal pairs of Young's inequality for subfactors, as well as the extremal operators of the Hausdorff-Young inequality.     

A Class of Optimally Conditioned Block 2 × 2 Matrices

A block 2 × 2 Hermitian positive-definite (h.p.d.) matrix is called equilibrated if its diagonal blocks coincide with the corresponding blocks of its inverse. It is demonstrated that any block 2 × 2 h.p.d. matrix is block diagonally similar to an equilibrated matrix, and any equilibrated matrix is optimally conditioned. Other properties of equilibrated matrices are also established. Bibliography: 8 titles.     

Moore-Penrose Inverses and Group Inverses of Block k-Circulant Matrices

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Inverse Spectrum Problems for Block Jacobi Matrix

By establishing the spectrum (matrix) function for the block Jacobi matrix, theorems of existence and uniqueness for the inverse problem and algorithms for its solution are obtained. The study takes into account all possible multiple-eigenvalue cases that are very difficult to deal with by other means.     

Block toeplitz operators with rational symbol analytic at infinity

This paper concerns the problem of explicit inversion of a block Toeplitz operator with rational and analytic at infinity symbol. The necessary and sufficient conditions for the invertibility and explicit formulas for the inverse are given in terms of the realization of the symbol.     

正定矩阵的Khatri-Rao乘积的块Schur补的逆的一些偏序

给出了分块矩阵的块Schur补的定义，得到一些正定矩阵的Khatri-Rao乘积的块Schur补的逆的偏序,推广了正定矩阵的Hadamare乘积的相应结果。     

Block decomposition of permutations and Schur-positivity

The block number of a permutation is the maximum number of components in its expression as a direct sum. We show that, for 321-avoiding permutations, the set of left-to-right maxima has the same distribution when the block number is assumed to be k, as when the last descent of the inverse is assumed to be at position \(n - k\). This result is analogous to the Foata–Schützenberger equidistribution theorem, and implies that the quasi-symmetric generating function of the descent set over 321-avoiding permutations with a prescribed number of blocks is Schur-positive.