共查询到20条相似文献,搜索用时 343 毫秒
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1 引言及记号用 Rn× n表示所有 n× n阶实矩阵的集合 ,用 Sn× n,Sn× n+及 Sn× n++分别表示所有 n×n实对称矩阵 ,实对称半正定矩阵及实对称正定矩阵的集合 ,用 Tr(M)表示矩阵 M的迹 ,对 A,B∈ Rn× n.定义其内积为 A×B=Tr(ATB) .考虑如下半正定线性互补问题 :求 X,Y∈ Sn× n使Y =L (X) +Q,X≥ O,Y≥ O,X× Y =0 ,(1)其中 Q∈ Sn× n,L :Sn× n→ Sn× n为线性算子 ,而 X≥ O表示 X∈ Sn× n+(O表示零矩阵 ) .若 L:Sn× n→Sn× n满足X× L (X)≥ 0 , X∈ Sn× n. (2 )则称其为单调算子 ,而相应的问题称为单… 相似文献
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考虑非线性矩阵方程X-A~*X~(-1)A=Q,其中A是n阶复矩阵,Q是n阶Hermite正定解,A~*是矩阵A的共轭转置.本文证明了此方程存在唯一的正定解,并推导出此正定解的扰动边界和条件数的显式表达式.以上结果用数值例子加以说明. 相似文献
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考虑非线性矩阵方程X-A*X-1A=Q,其中A是n阶复矩阵,Q是n阶Hermite正定解,A*是矩阵A的共轭转置.本文证明了此方程存在唯一的正定解,并推导出此正定解的扰动边界和条件数的显式表达式.以上结果用数值例子加以说明. 相似文献
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N—范数,M—最小二乘解的扰动理论 总被引:2,自引:1,他引:1
一 引言与预备知识 设A∈C~(mxn),M与N分别为m阶与n阶正定的Hermite矩阵。则存在唯一的矩阵X∈C~(n×m),满足 相似文献
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线性流形上Hermite-广义反Hamilton矩阵反问题的最小二乘解 总被引:8,自引:0,他引:8
1.引言 令Rn×m表示所有n×m实矩阵集合,Cn×m表示所有n×m复矩阵集合,Cn=Cn×1,HCn×n表示所有n阶Hermite矩阵集合,UCn×n表示所有n阶酉矩阵集合,AHCn×n表示所有n阶反Hermite矩阵集合,R(A)表示A的列空间,N(A)表示A的零空间,A+表示A的Moore—Penrose广义逆,A*B表示A与B的Hadamard积,rank(A)表示矩阵A的秩.tr(A)表示矩阵A的迹.矩阵A,B的内积定义为(A,B)=tr(BHA),A,B∈Cn×m,由此内积诱导的范数为||A||=√(A,A)=[tr(AHA)]1/2,则此范数为Frobenius范数,并且Cn×m构成一个完备的内积空间,In表示n阶单位阵,i=√-1,记OASRn×n表示n×n阶正交反对称矩阵的全体,即 相似文献
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We consider the only remaining unsolved case n≡0 (mod k) for the largest kth eigenvalue of trees with n vertices. In 1995, Jia-yu Shao gave complete solutions for the cases k=2,3,4,5,6 and provided some necessary conditions for extremal trees in general cases (cf. [Linear Algebra Appl. 221 (1995) 131]). We further improve Shao's necessary condition in this paper, which can be seen as the continuation of [Linear Algebra Appl. 221 (1995) 131]. 相似文献
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Marek Niezgoda 《Linear algebra and its applications》2009,431(8):1192-142
In this paper, singular values of commutators of Hilbert space operators are estimated. To this aim the accretivity of a transform of the operators is applied. Some recent results of Kittaneh [F. Kittaneh, Singular value inequalities for commutators of Hilbert space operators, Linear Algebra Appl. 430 (2009) 2362-2367] are extended. 相似文献
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It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices. 相似文献
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Proof of a conjecture of Fiedler and Markham 总被引:4,自引:0,他引:4
Xuerong Yong 《Linear algebra and its applications》2000,320(1-3):167-171
Let A be an n×n nonsingular M-matrix. For the Hadamard product AA−1, M. Fiedler and T.L. Markham conjectured in [Linear Algebra Appl. 10l (1988) 1] that q(AA−1)2/n, where q(AA−1) is the smallest eigenvalue (in modulus) of AA−1. We considered this conjecture in [Linear Algebra Appl. 288 (1999) 259] having observed an incorrect proof in [Linear Algebra Appl. 144 (1991) 171] and obtained that q(AA−1)(2/n)(n−1)/n. The present paper gives a proof for this conjecture. 相似文献
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This note provides a new approach to a result of Foregger [T.H. Foregger, On the relative extrema of a linear combination of elementary symmetric functions, Linear Multilinear Algebra 20 (1987) pp. 377–385] and related earlier results by Keilson [J. Keilson, A theorem on optimum allocation for a class of symmetric multilinear return functions, J. Math. Anal. Appl. 15 (1966), pp. 269–272] and Eberlein [P.J. Eberlein, Remarks on the van der Waerden conjecture, II, Linear Algebra Appl. 2 (1969), pp. 311–320]. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the proof in [Foregger, 1987] is flawed. 相似文献
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研究整环Z[3]上无限维矩阵V关于无限维矩阵构造下的逆、M-P逆和群逆,给出V的不同的逆、M-P逆等,推广了Saranya和Sivakumar的结果,并且得到Z[3]上无限维矩阵广义逆更广泛的性质. 相似文献
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In this note, we investigate characterizations for k-generalized projections (i.e., Ak = A*) on Hilbert spaces. The obtained results generalize those for generalized projections on Hilbert spaces in [Hong-Ke Du, Yuan Li, The spectral characterization of generalized projections, Linear Algebra Appl. 400 (2005) 313–318] and those for matrices in [J. Benítez, N. Thome, Characterizations and linear combinations of k-generalized projectors, Linear Algebra Appl. 410 (2005) 150–159]. 相似文献
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Jeffrey J. Hunter 《Linear algebra and its applications》2009,430(10):2607-907
The derivation of the expected time to coupling in a Markov chain and its relation to the expected time to mixing (as introduced by the author [J.J. Hunter, Mixing times with applications to perturbed Markov chains, Linear Algebra Appl. 417 (2006) 108-123] are explored. The two-state cases and three-state cases are examined in detail. 相似文献
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1引言 三对角矩阵出现在很多应用中,例如,在求解常系数微分方程的比值问题,三次样条插值等应用中都会遇到三对角矩阵.因此这类矩阵非常重要,而且也有很多学者致力于这类矩阵的研究.在一些应用中,比如估计条件数和构造稀疏近似逆预条件子,需要计算三对角矩阵的逆,或者估计其逆元素的界.文献[1-7]给出了关于三对角矩阵逆的一些很好的结果,但是,这些结果大都建立在矩阵对角占优的条件之下,这限制了他们的应用.在本文中,我们给出一种一般三对角矩阵逆元素的估计办法. 相似文献
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Yuki Seo 《Linear algebra and its applications》2000,320(1-3)
As a converse of the arithmetic–geometric mean inequality, W. Specht [Math. Z. 74 (1960) 91–98] estimated the ratio of the arithmetic mean to the geometric one. In this paper, we shall show complementary inequalities to the matricial generalization of Oppenheim's inequality and the Golden–Thompson type inequalities on the Hadamard product by T. Ando [Linear Algebra Appl. 26 (1979) 203; Linear Algebra Appl. 241–243 (1996) 105], in which Specht's ratio plays an important role. As an application, we shall obtain a complementary inequality to the Hadamard determinant inequality. 相似文献