共查询到20条相似文献,搜索用时 687 毫秒
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本给出并证明了若干个子空间的并以及两个子空间的基构成子空间的充要条件,从而本质地揭示了除子空间的交与和是构造新的予空间的方法外,集合的其它运算不能构造新的子空间,最后分析了子空间直和的两种不同定义的优缺点,指出了张禾瑞教材中子空间直和定义推广时应注意的一个问题。 相似文献
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本文讨论了有限空间Vn 中包含给定l维子空间Vl 的m 维子空间的计数问题,以及给定子空间Vm 与Vn 相交恰为l维子空间的计数问题 相似文献
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本讨论了有限空同V.中包古给定l维子空间V1的m维子空间的计数问题,以及给定子空问Vm与Vn相交恰为l维子空问的计数问题. 相似文献
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求向量到子空间的距离的方法 总被引:1,自引:0,他引:1
求向量到子空间的距离的方法张力宏(吉林四平师范学院数学系136000)设V是实数域R上n维线性空间,a∈V,W是V的子空间,a1,a2,…,ak是W的一组基.众所周知,求向量a到子空间W的距离d就是求一个向量β∈W使r=a-β此时d一叫.由于w一N。... 相似文献
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关于Bloch空间的子空间 总被引:1,自引:1,他引:0
本文给出了Bloch空间一类子空间的包含关系,并利用Hadamard缺项级数证明了这些关系是最好的.所获得的结果包含了Besov空间和Bloch空间的一些已知结论. 相似文献
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本文是在半开集理论中提出了S-Lindeloef空间的概念。指S-Lindeloef空间是S-紧空间的一种推广,并对该空间及其子空间所具有的性质进行了一些有益的讨论。 相似文献
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Cyclic subspace codes gained a lot of attention especially because they may be used in random network coding for correction of errors and erasures. Roth, Raviv and Tamo in 2018 established a connection between cyclic subspace codes (with certain parameters) and Sidon spaces. These latter objects were introduced by Bachoc, Serra and Zémor in 2017 in relation with the linear analogue of Vosper's Theorem. This connection allowed Roth, Raviv and Tamo to construct large classes of cyclic subspace codes with one or more orbits. In this paper we will investigate cyclic subspace codes associated to a set of Sidon spaces, that is cyclic subspace codes with more than one orbit. Moreover, we will also use the geometry of linear sets to provide some bounds on the parameters of a cyclic subspace code. Conversely, cyclic subspace codes are used to construct families of linear sets which extend a class of linear sets recently introduced by Napolitano, Santonastaso, Polverino and the author. This yields large classes of linear sets with a special pattern of intersection with the hyperplanes, defining rank metric and Hamming metric codes with only three distinct weights. 相似文献
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The FEAST eigenvalue algorithm is a subspace iteration algorithm that uses contour integration to obtain the eigenvectors of a matrix for the eigenvalues that are located in any user‐defined region in the complex plane. By computing small numbers of eigenvalues in specific regions of the complex plane, FEAST is able to naturally parallelize the solution of eigenvalue problems by solving for multiple eigenpairs simultaneously. The traditional FEAST algorithm is implemented by directly solving collections of shifted linear systems of equations; in this paper, we describe a variation of the FEAST algorithm that uses iterative Krylov subspace algorithms for solving the shifted linear systems inexactly. We show that this iterative FEAST algorithm (which we call IFEAST) is mathematically equivalent to a block Krylov subspace method for solving eigenvalue problems. By using Krylov subspaces indirectly through solving shifted linear systems, rather than directly using them in projecting the eigenvalue problem, it becomes possible to use IFEAST to solve eigenvalue problems using very large dimension Krylov subspaces without ever having to store a basis for those subspaces. IFEAST thus combines the flexibility and power of Krylov methods, requiring only matrix–vector multiplication for solving eigenvalue problems, with the natural parallelism of the traditional FEAST algorithm. We discuss the relationship between IFEAST and more traditional Krylov methods and provide numerical examples illustrating its behavior. 相似文献
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谭连生 《数学物理学报(B辑英文版)》1995,(3)
THEDISTURBANCELOCALIZATIONPROBLEMFORSINGULARSYSTEMSTanLiansheng(WuhanInst.ofMath.Sci.,Chin.Acad.ofSci.,Wuhan430071,China.)Abs... 相似文献
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This paper focuses on the density of the minimal subspaces generated by a class of discrete linear Hamiltonian systems. It is shown that the minimal subspace is densely defined if and only if the maximal subspace is an operator; that is, it is single valued. In addition, it is shown that, if the interval on which the systems are defined is bounded from below or above, then the minimal subspace is non-densely defined in any non-trivial case. 相似文献
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Fast inexact subspace iteration for generalized eigenvalue problems with spectral transformation 总被引:1,自引:0,他引:1
Fei Xue 《Linear algebra and its applications》2011,435(3):601-622
We study inexact subspace iteration for solving generalized non-Hermitian eigenvalue problems with spectral transformation, with focus on a few strategies that help accelerate preconditioned iterative solution of the linear systems of equations arising in this context. We provide new insights into a special type of preconditioner with “tuning” that has been studied for this algorithm applied to standard eigenvalue problems. Specifically, we propose an alternative way to use the tuned preconditioner to achieve similar performance for generalized problems, and we show that these performance improvements can also be obtained by solving an inexpensive least squares problem. In addition, we show that the cost of iterative solution of the linear systems can be further reduced by using deflation of converged Schur vectors, special starting vectors constructed from previously solved linear systems, and iterative linear solvers with subspace recycling. The effectiveness of these techniques is demonstrated by numerical experiments. 相似文献
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本文引入了Banach代数上线性映射的Lie不变子空间,给出了因子VonNeumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一般形式,研究了Lie导子与Lie自同构的概念及了Lie导子与Lie自同构半群的关系. 相似文献
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P. Favati G. Lotti O. Menchi F. Romani 《Journal of Computational and Applied Mathematics》2007,210(1-2):191-199
In this paper we consider the problem of approximating the solution of infinite linear systems, finitely expressed by a sparse coefficient matrix. We analyse an algorithm based on Krylov subspace methods embedded in an adaptive enlargement scheme. The management of the algorithm is not trivial, due to the irregular convergence behaviour frequently displayed by Krylov subspace methods for nonsymmetric systems. Numerical experiments, carried out on several test problems, indicate that the more robust methods, such as GMRES and QMR, embedded in the adaptive enlargement scheme, exhibit good performances. 相似文献
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R. J. Stern 《Journal of Optimization Theory and Applications》1978,25(1):105-115
In a linear control system setting, we derive conditions under which extremal controls give rise to trajectories which exit a given subspace. An application is in determining effectiveness of linear state restraints in time-optimal problems.This work was supported by the National Research Council of Canada under Grant No. A4641. 相似文献
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闭极大线性子空间正交补的唯一性 总被引:2,自引:2,他引:0
研究赋范线性空间中闭极大线性子空间的正交可补性.利用空间的对偶映射给出固定闭极大线性子空间至多存在一个正交补的充分必要条件,从而给出每个闭极大线性子空间至多存在一个正交补的几何刻画. 相似文献