The definition of pseudoframes for subspaces is given.
引进广义多分辨结构与子空间伪框架的概念。
In this paper, a fundamental identity for frames of subspaces is introduced.
本文研究了子空间框架的一个基本恒等式。
So one can study the signal in some much lower-dimensional subspaces, specifically, some planes.
事实上，经过坐标变换，我们可以在维数更低的子空间（甚至是在平面上）来研究信号。
In an infinite dimensional space there always exist two subspaces whose vector sum is different from their span.
在一无限空间中恒存在两个子空间，其矢量和与其张成空间不同。
The most popular methods to solve large sparse problems are based on projection techniques on appropriate subspaces.
求解大型稀疏问题最流行的方法是建立在子空间投影技术之上的。
We proved orthocompactness and weakly suborthocompactness are equivalent for all subspaces of product of two GO-space.
证明了GO-空间子空间的正交紧性和弱子正交紧性是等价的。
In the third chapter, the perturbation of invariant subspace, singular subspaces and deflating subspaces are discussed.
第三章讨论了不变子空间、奇异子空间对和收缩子空间对的扰动。
It is proved that the (a, b) invariant subspaces can be always decomposed into a direct-sum form of some radical subspaces.
证明了任意一个(A,B)不变子空间一定能分解成一些根子空间的直和。
So a FR algorithm is designed by fusing holistic and local features in subspaces, which is inspired by Human Visual System (HVS).
本文模仿人类视觉系统的特点，提出了融合局部和整体特征子空间的算法。
However, among the active subspaces, some of them do not contain any query results at all, those are called false active subspaces.
但是在活动子空间中，有些可能根本就不包含任何查询结果，这样的活动子空间被称为假活动子空间。
In the linear space with descending chain condition of subspaces, every subspace can be written as finite intersection of maxmin subspaces.
在满足子空间降链条件的线性空间中，每个子空间可表示为有限个极大子空间的交。
A general difficulty of using singular value decomposition (SVD) to split signal and noise subspaces is in the right choice of effective rank.
用奇异值分解界定信号和噪声子空间的困难之处，在于有效秩的确定。
The cheapest way to get one is to invoke the spectral theorem and to conclude that normal operators always have non-trivial invariant subspaces.
尝试是引用光谱定理而得到正规算子恒有非平凡不变子空间的结论。
Lastly, the characteristics between fault outputs and measuring inputs in different subspaces have been obtained by processing off line learning.
最后，通过离线学习获得不同子空间故障输出与测量输入的非线性动力特性。
Perturbation analysis of the canonical subspaces: This paper gives the least perturbation bound of the unitary factor on the unitary decomposition.
标准子空间的扰动分析：本文给出了矩阵的酉分解中酉因子的最小扰动界。
Information on the steering vector is not exploited when estimating signal or noise subspaces in the standard multiple signal classification (MUSIC) method.
常规多信号分类(MUSIC)在估计信号或噪声子空间时未利用阵列的方向矢量信息。
In the direction of arrival (DOA) estimation problem, the relationship between the second-order and the fourth-order subspaces is found and proved in the paper.
本文分析了在高阶统计应用阵来波方向估计问题中二阶子空间与四阶子空间的概念及形式关系。
Several types of spline multiresolution analyses are constructed systematically simply based on the general decomposition theory of two-scale shift-invariant subspaces.
本文根据平移不变子空间二尺度分解理论，系统、简结地构造了各类样条多分辨分析。
Optimal signal subspace is the foundation for our adaptive modulation algorithms in SC-FDE. Another new concept is introduced called sequenced optimal signal subspaces.
最优信号子空间的思想是SC - FDE中设计自适应调制算法的根本基础，在此基础上又提出了序列最优信号子空间的概念。
Through estimating the signal and noise subspaces with the eigen-decomposition of the correlation matrix, the MUSIC algorithm is used to estimate the DOAs of LFM sources.
通过对相关矩阵进行特征值分解，估计信号子空间和噪声子空间，并利用MU S IC算法估计宽带LF M信号的波达方向。
The electrocardiogram(ECG) is decomposed on the single value decomposition(SVD) into two time orthogonal subspaces, one containing ECG and the other containing artifacts.
ECG经奇异值正交分解后，将信号分解到信号空间和噪声空间中。
Besides, the author gives the necessary and sufficient conditions for the two generating subspaces to be orthogonal complement spaces in a unitary space and certain corollaries.
在此基础上，得到了酉空间中两个生成子空间互为正交补空间的充要条件及其若干推论。
In the similarity query processing based on high dimensional indexing, the searching space is usually narrowed down by pruning the inactive subspaces which do not contain any query results.
在基于高维索引技术的相似性查询处理中，通常通过过滤那些不包含任何查询结果的非活动子空间来不断缩减搜索空间。
The paper points out that the key for performing the DOA estimation, using subspace method, is as follows: a) how to divide the space expanded by an array into the signal and noise subspaces;
指出了用子空间方法进行DOA估计的关键是：第一，如何将基阵张成的空间划分为信号子空间和噪声子空间；第二。
It is proved that for sufficiently good subspaces the approximate singular values obtained by the harmonic projection methods converge while the corresponding approximate singular vectors may not.
本文证明了，当投影空间足够好时，该方法得到的近似奇异值收敛，但近似奇异向量可能收敛很慢甚至不收敛。
The design of complex system can be non-hierarchically decomposed into several parallel subspace design tasks, and the multidisciplinary optimization can be considered as the game of the subspaces.
复杂系统的设计问题可以非层次分解为并行的多个子空间优化设计问题。
The design of complex system can be non-hierarchically decomposed into several parallel subspace design tasks, and the multidisciplinary optimization can be considered as the game of the subspaces.
复杂系统的设计问题可以非层次分解为并行的多个子空间优化设计问题。
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