共查询到20条相似文献,搜索用时 187 毫秒
1.
用数学归纳法推出了可逆矩阵的高次伴随矩阵的公式,并结合可逆矩阵的基本公式得出了可逆矩阵的高次伴随矩阵的行列式和逆矩阵,给出了可逆矩阵的高次伴随矩阵的特征值和特征向量的表示公式,最后讨论了若干个可逆矩阵的乘积的高次伴随矩阵. 相似文献
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用Riordan矩阵的方法研究了具有4种步型的加权格路(广义Motzkin路)的计数问题,引入了一类新的计数矩阵,即广义Motzkin矩阵.同时给出了这类矩阵的Riordan表示,也得到了广义Motzkin路的计数公式.Catalan矩阵,Schrder矩阵和Motzkin矩阵都是广义Motzkin矩阵的特殊情形. 相似文献
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本文利用矩阵运算、矩阵相似关系及矩阵的秩,深化了Jordan矩阵的性质,并在此基础上刻画了矩阵Jordan标准形中Jordan块的个数及阶数,最后讨论了矩阵多项式Jordan标准形,充实了高等代数中Jordan标准形的结果. 相似文献
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提出了一种求三对角与五对角Toeplitz矩阵逆的快速算法,其思想为先将Toeplitz矩阵扩展为循环矩阵,再快速求循环矩阵的逆,进而运用恰当矩阵分块求原Toeplitz矩阵的逆的算法.算法稳定性较好且复杂度较低.数值例子显示了算法的有效性和稳定性,并指出了算法的适用范围. 相似文献
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非奇异矩阵的逆是矩阵元素的连续函数.学者们也对矩阵广义逆的连续性有所研究.本文应用矩阵分裂和两个矩阵之和的逆的展开式,给出了一般非奇异矩阵,M-矩阵和H-矩阵的逆的连续性.当一些合理的条件满足时,这几种矩阵的逆是连续的. 相似文献
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揭示几类矩阵之间的紧密联系.借助于群的子群的判定以及循环布尔矩阵是本原矩阵的判定方法,得到循环模糊矩阵成为幂等矩阵的充要条件,反循环布尔矩阵成为本原矩阵的充要条件.并给出了循环模糊矩阵成为幂等矩阵的判定方法,反循环布尔矩阵成为本原矩阵的判定方法. 相似文献
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广义正定矩阵的进一步研究 总被引:2,自引:1,他引:1
基于正定矩阵的几个定义,首先给出了广义正定矩阵的一些新性质,其次研究了广义正定矩阵与H-矩阵、M-矩阵的关系,推广和改进了文献中的有关行列式不等式. 相似文献
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胡瑞平 《应用数学与计算数学学报》1999,13(2):83-86
设Ai,Bi,Gi为给定的矩阵,i=1,2,S为||A1XB1-C1||2F+||A2XB2-C2||2F=min的解集,在给定矩阵X0的条件下,求X∈S;使得本文利用[6]的结果给出了X的表达式. 相似文献
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Liczberski-Starkov first found a lower bound for ||D(f)|| near the origin, where is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ||D(f)|| is obtained again. 相似文献
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设L(R~n)表示n维欧氏空间R~n的所有线性变换构成的集合,‖ξ‖表示向量ξ的欧氏长度,由欧氏长度建立起向量间的序关系,令:PO(R~n)={f∈L(R~n)■|ξ,η∈R~(n×1),‖ξ‖≤‖η‖■‖f(ξ)‖≤‖f(η)‖}则PO(R~n)是欧氏空间R~n中保欧氏度量偏序变换构成的集合,讨论了PO(R~n)的结构,证明了保持这种序关系的变换由正交变换和伸缩变换组成. 相似文献
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In this paper, we study the perturbation bounds for the polar decomposition A= QH where Q is unitary and H is Hermitian. The optimal (asymptotic) bounds obtained in previous works for the unitary factor, the Hermitian factor and singular values of A are σ2r||△Q||2F ≤ ||△A||2F,1/2||△H||2F ≤ ||△A||2F and ||△∑||2F ≤ ||△A||2F, respectively, where ∑ = diag(σ1, σ2,..., σr, 0,..., 0) is the singular value matrix of A and σr denotes the smallest nonzero singular value. Here we present some new combined (asymptotic)perturbation bounds σ2r ||△Q||2F+1/2||△H||2F≤ ||△A||2F and σ2r||△Q||2F+||△∑ ||2F ≤||△A||2F which are optimal for each factor. Some corresponding absolute perturbation bounds are also given. 相似文献
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A perturbation bound for the Drazin inverse AD with Ind(A+E)=1 has recently been developed. However, those upper bounds are not satisfied since it is not tight enough. In this paper, a sharper upper bounds for ||(A+E)#−AD|| with weaker conditions is derived. That new bound is also a generalization of a new general upper bound of the group inverse. We also derive a new expression of the Drazin inverse (A+E)D with Ind(A+E)>1 and the corresponding upper bound of ||(A+E)D−AD|| in a special case. Numerical examples are given to illustrate the sharpness of the new bounds. 相似文献
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L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,127(3):1969-1975
The lower bound
l1 (A) - ln (A) \geqslant 2||A12 ||\lambda _1 (A) - \lambda _n (A) \geqslant 2\parallel A_{12} \parallel 相似文献
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Ji-Guang Sun 《BIT Numerical Mathematics》1997,37(1):179-188
Consider the linear least squares problem min x ‖b?Ax‖2 whereA is anm×n (m<n) matrix, andb is anm-dimensional vector. Lety be ann-dimensional vector, and let ηls(y) be the optimal backward perturbation bound defined by $$\eta _{LS} (y) = \inf \{ ||F||_F :y is a solution to \mathop {min}\limits_x ||b - (A + F)x||_2 \} .$$ . An explicit expression of ηls(y) (y≠0) has been given in [8]. However, if we define the optimal backward perturbation bounds ηmls(y) by $$\eta _{MLS} (y) = \inf \{ ||F||_F :y is the minimum 2 - norm solution to \mathop {min}\limits_x ||b - (A + F)x||_2 \} ,$$ , it may well be asked: How to derive an explicit expression of ηmls(y)? This note gives an answer. The main result is: Ifb≠0 andy≠0, then ηmls(y)=ηls (y). 相似文献
20.
Nicolas Templier 《Selecta Mathematica, New Series》2010,16(3):501-531
We establish upper bounds for the sup-norm of Hecke-Maass eigenforms on arithmetic surfaces. In a first part, the case of
open modular surfaces is studied. Let f{f} be an Hecke–Maass cuspidal newform of square-free level N{N} and bounded Laplace eigenvalue. Recently, V. Blomer and R. Holowinsky [Invent. Math., 179 (3)] provide a non-trivial bound
when f{f} is non-exceptional. Our approach is different in that we rely on the geometric side of the trace formula. The improved bound
||f||¥ << N-1/23 ||f||2{||f||_\infty \ll N^{-1/23} ||f||_2} is established. In a second part, we show that a corresponding result holds true for compact arithmetic surfaces and with
a better exponent 1/12. The proof requires an estimate for the number of lattice points in a certain annulus domain. A key
input is that a congruence subgroup (multiplicative group) is included in an order (ring). This structure enables us to introduce
a diophantine argument. 相似文献
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