共查询到20条相似文献,搜索用时 46 毫秒
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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. 相似文献
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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′AX0(>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... 相似文献
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Toeplitz-Bezout矩阵的若干性质 总被引:1,自引:0,他引:1
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. 相似文献
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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. 相似文献
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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. 相似文献
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郑建青 《纯粹数学与应用数学》2014,(1):45-52
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. 相似文献
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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. 相似文献
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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.
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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. 相似文献
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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. 相似文献
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