矩阵酉扩张的刻划

本文用奇异值刻划了具有指定阶酉扩张的矩阵类，同时讨论了矩阵的正规扩张问题     

一致概周期矩阵函数的一些性质

利用纯量概周期函数性质讨论了一致概周期矩阵函数的一些性质.     

循环矩阵的一些性质

本文给出了循环矩阵的一些性质.     

Hadamard乘积矩阵的一些性质

本文给出了Ｈａｄａｍａｒｄ乘积矩阵的秩和行列式的两个不等式     

既约随机矩阵的一些性质

本文讨论了既约广义随机矩阵特征值的性质,得到了双随机矩阵的益为既约矩阵的充要条件,以及P类矩阵的一些性质．     

关于斜正定矩阵的一些性质

利用矩阵的次转置共轭和翻转矩阵等技巧,给出关于斜正定矩阵的一些性质,给出矩阵的斜对称部分与其逆之差是斜半正定的结论.     

非对称半正定矩阵的一些性质

非对称半正定矩阵的一些性质阳本傅（成都师范高等专科学校数学系６１１９３０）设Ａ是ｎ阶实矩阵（不一定对称），如果对任意实ｎ元向量Ｘ，均有Ｘ′ＡＸ０（＞０），就称Ａ为半正定矩阵（正定矩阵）．本文给出半正定矩阵的一种合同标准形，由此比较简捷地得出了半正定...     

Toeplitz-Bezout矩阵的若干性质

从定义出发,利用矩阵生成函数的方法来研究Toeplitz-Bezout若干基本性质,同时利用极限的思想将其对角约化.     

灰对角矩阵的一些性质

本文根据灰对角矩阵的定义．得到一些性质．     

三幂等矩阵的一些性质

重点探索了三幂等矩阵的性质.主要从矩阵乘积、线性变换和矩阵的秩等角度出发,将幂等矩阵的性质向三幂等矩阵推广,对三幂等矩阵的性质进行探究,得到了15个相关结论,并给出部分性质的详细推导过程.     

Some properties of the positive real matrix

In this paper, some properties of the rational positive real matrix are discussed by means of coprime fraction of a rational matrix. Some equivalent conditions which are natural extension of the rational positive real function, are given for testing a rational positive real matrix.     

次正定复矩阵次Schur补的一些性质

利用复矩阵的Schur补和次正定性,研究了次正定复矩阵的次Schur补的一些性质,得到了次正定复矩阵次Schur补的几个行列式不等式,将相关文献的相应结果由次正定次Hermite矩阵推广到次正定复矩阵.     

Dynamical properties of expansive one-sided cellular automata

To every one-sided one-dimensional cellular automatonF with neighbourhood radiusr we associate its canonical factor defined by considering only the firstr coordinates of all the images of points under the powers ofF. Whenever the cellular automaton is surjective, this factor is a subshift which plays a primary role in its dynamics. In this article we study the class of positively expansive one-sided cellular automata, i.e. those that are conjugate to their canonical factors. This class is a natural generalisation of the toggle or permutative cellular automata introduced in [He]. We prove that the canonical factors of positively expansive one-sided cellular automata are mixing subshifts of finite type that are shift equivalent to full shifts. Moreover, the uniform Bernoulli measure is the unique measure of maximal entropy forF. Consequently, their natural extensions are Bernoulli. We also describe a family of non-permutative positively expansive cellular automata. This research was partially supported by action E9314 of ECOS-CONICYT.     

Some geometric properties of matrix means with respect to different metrics

In this paper we study the monotonicity, in-betweenness and in-sphere properties of matrix means with respect to Bures–Wasserstein, Hellinger and log-determinant metrics. More precisely, we show that the matrix power means (Kubo–Ando and non-Kubo–Ando extensions) satisfy the in-betweenness property in the Hellinger metric. We also show that for two positive definite matrices A and B, the curve of weighted Heron means, the geodesic curve of the arithmetic and the geometric mean lie inside the sphere centered at the geometric mean with the radius equal to half of the log-determinant distance between A and B.

     

Some properties of invariant polynomials with matrix arguments and their applications in econometrics

Summary Further properties are derived for a class of invariant polynomials with several matrix arguments which extend the zonal polynomials. Generalized Laguerre polynomials are defined, and used to obtain expansions of the sum of independent noncentral Wishart matrices and an associated generalized regression coefficient matrix. The latter includes thek-class estimator in econometrics.     

Some matrix functional equations

We investigate the pair of matrix functional equations G(x)F(y) = G(xy) and G(x)G(y) = F(y/x), featuring the two independent scalar variables x and y and the two N×N matrices F(z) andG(z) (with N an arbitrary positive integer and the elements of these two matrices functions of the scalar variable z). We focus on the simplest class of solutions, i.e., on matrices all of whose elements are analytic functions of the independent variable. While in the scalar (N = 1) case this pair of functional equations only possess altogether trivial constant solutions, in the matrix (N > 1) case there are nontrivial solutions. These solutions satisfy the additional pair of functional equations F(x)G(y) = G(y/x) andF(x)F(y) = F(xy), and an endless hierarchy of other functional equations featuring more than two independent variables.