摘要翻译:
考虑形式为$\bf{A}+(\bf{V}_1+\bf{W}_1)\bf{G}(\bf{V}_2+\bf{W}_2)^*$的矩阵,其中$\bf{A}$是一个$奇异的$$\ell\乘以\ell$矩阵,$\bf{G}$是非奇异的$k\乘以k$矩阵,$k\le\ell$。设$\bf{V}_1$的列位于$\bf{A}$的列空间中,$\bf{W}_1$的列与$\bf{A}$正交。类似地,设$\bf{V}_2$的列位于$\bf{A}^*$的列空间中,$\bf{W}_2$的列与$\bf{A}^*$正交。在$\bf{W}_i^*\bf{W}_i$具有秩$k$的前提下,给出了逆的显式表达式。%和$\bf{W}_1$和$\bf{W}_2$具有相同的列空间。给出了协方差矩阵关于均值定心的一个应用。
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英文标题:
《A Sherman-Morrison-Woodbury Identity for Rank Augmenting Matrices with
Application to Centering》
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作者:
Kurt S. Riedel
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最新提交年份:
2018
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分类信息:
一级分类:Statistics 统计学
二级分类:Methodology 方法论
分类描述:Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计,调查,模型选择,多重检验,多元方法,信号和图像处理,时间序列,平滑,空间统计,生存分析,非参数和半参数方法
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一级分类:Computer Science 计算机科学
二级分类:Numerical Analysis 数值分析
分类描述:cs.NA is an alias for math.NA. Roughly includes material in ACM Subject Class G.1.
cs.na是Math.na的别名。大致包括ACM学科类G.1的材料。
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一级分类:Computer Science 计算机科学
二级分类:Systems and Control 系统与控制
分类描述:cs.SY is an alias for eess.SY. This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
cs.sy是eess.sy的别名。本部分包括理论和实验研究,涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制,以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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一级分类:Electrical Engineering and Systems Science 电气工程与系统科学
二级分类:Systems and Control 系统与控制
分类描述:This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
本部分包括理论和实验研究,涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制,以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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一级分类:Mathematics 数学
二级分类:Functional Analysis 功能分析
分类描述:Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间,函数空间,实函数,积分变换,分布理论,测度理论
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一级分类:Mathematics 数学
二级分类:Numerical Analysis 数值分析
分类描述:Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法,科学计算
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一级分类:Mathematics 数学
二级分类:Spectral Theory 光谱理论
分类描述:Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
薛定谔算子,流形上的算子,一般微分算子,数值研究,积分算子,离散模型,共振,非自伴算子,随机算子/矩阵
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英文摘要:
Matrices of the form $\bf{A} + (\bf{V}_1 + \bf{W}_1)\bf{G}(\bf{V}_2 + \bf{W}_2)^*$ are considered where $\bf{A}$ is a $singular$ $\ell \times \ell$ matrix and $\bf{G}$ is a nonsingular $k \times k$ matrix, $k \le \ell$. Let the columns of $\bf{V}_1$ be in the column space of $\bf{A}$ and the columns of $\bf{W}_1$ be orthogonal to $\bf{A}$. Similarly, let the columns of $\bf{V}_2$ be in the column space of $\bf{A}^*$ and the columns of $\bf{W}_2$ be orthogonal to $\bf{A}^*$. An explicit expression for the inverse is given, provided that $\bf{W}_i^* \bf{W}_i$ has rank $k$. %and $\bf{W}_1$ and $\bf{W}_2$ have the same column space. An application to centering covariance matrices about the mean is given.
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PDF链接:
https://arxiv.org/pdf/1803.10405