正交补

In light of orthogonality, we define and discuss orthogonal complement of a set in a Banach space.

进一步，我们引入了正交补的概念，讨论了Birkhoff正交补的相关问题。

Based on the kernel trick in Support Vector Machine, the orthogonal complementary space method based on kernel trick is presented finally in this paper.

基于核的正交补空间法先在原始样本里利用核技术，在变换后的特征空间里，借鉴文献[41]的正交补空间思想抽取用于鉴别分析的特征。

Firstly, based on the stability criterion for the nominal discrete singular time-delay system, a sufficient condition for the existence of the static output feedback controller in terms of linear matrix inequality with linear matrix equality constraint is established, which ensures that the resulting closed-loop system is regular, causal and robustly asymptotically stable, and the static output feedback controller is designed by the feasible solution of the linear matrix inequality with linear matrix equality constraint.

首先基于标称离散广义时滞系统的稳定条件，以受限线性矩阵不等式形式，得到闭环离散广义时滞系统正则、因果且渐近稳定的充分条件，同时利用受限矩阵不等式的可行解给出静态输出反馈控制器的设计方法；然后采用矩阵的正交补，把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式的可行解；最后的数值实例说明了所给方法的有效性和正确性。

Let G be semisimple matrix group with Lie algebra g, T a fixed maximal abelian subalgebra of g, T the orthogonal complement of T with respect to the Killing form of g, and a, b 6 T a fixed regular elements.

设G为半单矩阵群，g为其Lie代数，T(来源：ABC论文91网www.abclunwen.com)为g的极大交换子代数，T~⊥为T关于g的Killing型的正交补，a，b∈T为固定正则元。

By its definition, we know it has consanguineous relation with isometry, thus we can study isometry to investigate it. The emphase of the chapter is to study Isosceles orthogonal complementary, and use it to study geometrical properties of Banach space.

接着引入并研究了Isosceles正交补的有关问题，并由此研究了Banach空间的一些重要几何性质。

An algorithm is presented that trasforms the problem from the orthocomplement space to a general finite element subspace.

提出了一种实施算法，把问题的求解从正交补空间转化到普通有限元子空间，且公式简单，求解方便易行。

Kinetic equations of multibody systems with scleronomic constraint s are projected along the feasible and unfeasible directons of the constiaints respectively,and generalized accelerations of the systems are decomposed along the two directons using the bases of constraint matrix and its orthocomplement.

通过约束矩阵及其正交补的两组基，将定常约束多体系统的动力学方程沿与约束相容和不相容的两个方向上投影，并将系统的广义加速度沿这两个方向进行分解，得到描述系统运动的纯微分方程和求约束力的公式，同时提出了违约修正的一种方法。

Chapter 3 discusses the algebraic and spectral properties of dual Toeplitz operators on the orthogonal complement of the Bergman space, such as boundedness, compactness, spectral properties and so on.

第三章研究了多圆盘Bergman空间的正交补空间L_a~2(D~n~⊥上对偶Toeplitz算子的代数性质，比如：有界性、紧性和谱性质等。

In this paper, some decision theorems are suggested about the matrix orthogonal problem on the subspace of the finite dimensional Euclidan subspace. In addition, some concise results are obtained by matrix representation of the orthogonal complement and injection of vectors on the subspace.

利用向量组的Gram矩阵和向量的坐标矩阵对有限维欧氏空间中子空间的正交性给出了矩阵判定条件，对子空间的正交补及向量在子空间上的内射影给出了矩阵表示，获得了一些简捷有用的结果。

Particularly,when A is positive,we give a detailed characterization of the set ∏={Q∈∏:R=S⊥,AQ=QA},where ∏ and S⊥ denote the set of all idempotents on H and the orthogonal complement of S,respectively.

特别地，当A是正算子时得出了集合∏={Q∈∏：R=S⊥，AQ=Q*A}非空的充要条件；并且对集合∏进行了详细的刻化，这里∏和S⊥分别表示一个复Hilbert空间上的所有幂等算子构成的集合和子空间S的正交补空间。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。