查询词典 vector subspace

The generalized minimal error method for solving large linear systems minimizes the Euclidean norm of the error in the related generalized Krylov subspace, and is one of Krylov subspace methods for solving large linear system Ax = b.

广义最小误差方法是求解大型线性方程组Ax = b的一个Krylov子空间方法，使误差范数在Krylov子空间上达到最小，。

In SLDMINV the invariance of the Krylov subspace is invoked, making the main computation reduced into almost real arithmetic, and thus lowering the computation amount markedly. In the meantime, the iteration is performed in the Krylov subspace generated from the inverse of the coefficient matrix and so the convergent speed is enhanced greatly, leading to two orders of the magnitude improvement over standard SLDM.

SLDMINV中运用了Krylov子空间不变性技巧，这使得计算基本化为实运算，显著降低了计算量；同时在由系数矩阵的逆构成的子空间上进行迭代，收敛速度大大加快，较之SLDM提高两个量级。

The key technique in the MUSIC algorithm is the signal subspace extraction which can be found from the eigen decomposition of the sample covariance matrix of the antenna receive signal. The eigen value decomposition of a Hermitian matrix is implemented by using the QR algorithm, and the signal subspace is constituted by collecting the significant eigen vectors.

在复合信号分类演算法中的重要关键为信号子空间与杂讯子空间的分解，这两个子空间可以利用对天线收到信号的取样共变异矩阵做特徵值分解中求出，本篇并以QR演算法实现厄米特矩阵之特徵值分解，信号子空间便是由分解后的特徵向量所集合而成。

To detect more targets, the whitened data Z are projected onto the orthogonal subspace of w using the orthogonal subspace projector P⊥= W I .W.1WT, to eliminate the detected target, where I is an L×L identity matrix and W =.

为了要发现较多的目标，被数据白的 Z 被在 w 的直角次空间之上使用直角的次空间投光器 P 第一⊥= W 计画。W。，除去那发现了我是 L × L 身份点阵式和 W=的目标。

In particular, the paper gives a new description of the largest simultaneous invariant subspace contained in a given subspace H.

特别对 包含在给定子空间H中的最大同时不变子空间给出了新的描述。

Every reducible subspace of $T$ is invariant subspace of $T$ too.

人们自然相信，有不变子空间的算子可能有共轭。

Based on the invariability of the sought for chemical subspace to the linear transformation, a novel approach, called chemical subspace invariant to linear transformation method, is developed for estimation of chemical rank of two way data matrices.

提出了一个新的化学计量学方法，即线性变换下稳定的化学子空间法，用于二维数据的化学秩估计。

The well-known invariant subspace problem is A long-standing problem in operator theory,which has been to determine whether every operator $T$ on a Banach space $X$ must have a nontrivial invariant subspace.

不变子空间问题是一个尚未解决的问题， Enflo反例所给出的没有不变子空间的算子不为任何算子的共轭。

Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced.And some basic properties, such as separation lemma, were presented.

其次，引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念，给出一些有关概念的基本性质，特别是分离引理。

Equivalently, it can be raised as follows: for an A operator T, if M and N are two invariant subspaces of T satisfying N include M and dimN/M=∞, then does there exist another invariant subspace L such that N include L, and L include M ? It is rather difficult to study the invariant subspace problem of general diagonal operators.

研究表明它可以约化为对角算子的不变子空间的情形，具体地它有如下的等价提法：对于A算子算T，，如果M和N是T的两个不变子空间，满足且dimN/M=∞，那么是否存在T的另一个不变子空间L使得M包含于L，且L包含于N？

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。