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除环上rcf方阵的逆方阵 总被引:2,自引:0,他引:2
陈国龙 《高校应用数学学报(A辑)》2000,15(3):260-264
讨论了除环R上rcf方阵的逆方阵问题,证明了除环R上rcf方阵各种逆方阵存在的充分必要条件。 相似文献
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引入了本原无限布尔方阵的概念,给出了无限布尔方阵为本原阵的一个充分必要条件,最后给出了一类本原无限布尔方阵的本原指数集的刻划. 相似文献
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研究了定义域为对角形的上三角无穷维Hamilton算子:H=的谱刻画及其可逆性;当A的剩余谱不含关于虚轴对称的点时,H的谱等于A的谱与A的谱关于虚轴对称分支的并集,并得到了H的预解集为空及其可逆的充要条件;作为结论的应用,得到当A为无穷维Hamilton算子时,H的点谱、剩余谱、连续谱和谱分别等于A的点谱、剩余谱、连续谱和谱. 相似文献
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1 IntroductionConsider the following functional differential equationX'(t) = A(t)x(t) [' C(t,s)x(s)ds, (1)icwhere x E m; A(t) = (ail(t))... is a n x n function matrix, which continuesin [0, co); C(t,s) = (qj(t,8))... is a n x n function matrix, which conti-nues when 0 5 s 5 t < co, and L oo IIC(u,t)lldu continues in [0, co).The problem on the stability for the zero solution of (1) has been studied bymany papers. But in the known results, the boundedness of j: IIC(t, s)lldsor L " IIC… 相似文献
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In this paper, the sensitivity of the solution for a class of quadratic matrix equation which arises in the analysis of structural systems and vibration problems is discussed. With Brouwer fixed piont theory, the perturbation of the quadratic matrix equation is analyzed and two computational perturbation bounds are derived. Then a Rice condition number of some kind of solutions is given using the analytic expansion method. Two examples are presented in the last part. 相似文献
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Xie Minyu 《数学年刊B辑(英文版)》1994,15(4):435-442
Let X1,…XN(where N>m)be independent Nm(μ,∑)random vectors,and put X^-=1/N ∑i=1^N Xi and T‘T=A=∑i=1^N(Xi-X^-)(Xi-X^-)‘,where T is upper-triangular with positive diagonal elements.The author considers the problem of estimating ∑,and restricts his attention to the class of estimates D={T‘△^*T+Nb^*X^-X^‘·△^* is any diagonal matrix and b^* is any nonnegative constant}because it has the following attractive features:(a)Its elements are all quadratic forms of the sufficient and complete statistics(X^-,T).(b)It contains all estimates of the form αA+NbX^-X^-‘(α≥0 and b≥0),which construct a complete subclass of the class of nonnegative quadratic estimates D^8={X‘BX:B≥0}(where X=(X1,…,XN)‘)for any strict convex loss function.(c)It contains all invariant estimates under the transformation group of upper-triangular matrices.The author obtains the characteristics for an estimate of the form.T‘△T+NbX^-X^-‘(△=diag{δ1,…,δm}≥0 and b≥0)of ∑ to be admissible in D when the loss function is chosen as tr(∑^-1∑-I)^2,and shows,by an example,that αA+NX^-X^-‘(α≥0 and b≥0)is admissible in D^* can not imply its admissibility in D. 相似文献
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矩阵方程XTAX=B的一类反问题 总被引:3,自引:0,他引:3
1引言 本文用Rn×m表示所有n×m实矩阵全体;SR0n×n表示所有n阶实对称半正定矩阵全体;In表示n阶单位矩阵;A-,A+分别表示矩阵A的一个广义逆和Moore-Penrose广义逆;A≥0表示A为对称半正定矩阵;Sn=(en,en-1,…,e1)∈Rn×n,其中ei为单位阵In的第i列; [n/2]表示不超过n/2的最大整数. 相似文献