查询词典 inner product space

Based on the projection theorem in the finite-dimensional inner product space, by making use of the generalized singular value decomposition and the canonical correlation decomposition of matrix pair simultaneously, we transform the least-squares problems of the abovementioned inconsistent matrix equations into the problems of solving the consistent matrix equations over given matrix set, and obtain the general expressions of the corresponding least-squares solutions.

S使得‖-X~*‖=‖-X~*‖，其中‖·‖为Frobenius范数，S分别表示矩阵方程 AXB=D，AXA~T+BYB~T=D，AXB+CYD=E和矩阵方程组=，=在一般矩阵集合或对称矩阵集合上不相容时的最小二乘解集合。

Thesolutions compose self-contained inner product space (weight function is constant 1),i.e., they are basic series of Hilbert space; hence any internal waves could beexpanded into generalized Fourier series. With difference method, Sturm-Liouvilleequation is transformed to matrix eigenvalue problem. Each eigenvalue is related to ahorizontal wave number, and relevant solution is a certain mode of internal wave.

其解系构成完备的加权(权函数为1)内积空间，即Hilbert空间，从而内波现象可以展成该解系的广义Fourier级数；采用差分方法，将 Sturm-Liouville 方程转化为矩阵特征值问题，每一个特征值对应一个内波波数，该特征值对应的解则是内波的某一模态。

At the same time, the values range of two kinds of nonsquare constants and their values in real inner product space are given .

同时给出了两种点态非方常数的取值范围，和实内积空间中两种点态非方常数的值。

So an inner product space is automatically a normed linear space, and a Hilbert space is automatically a Banach space.

我们定义了线性映射的厄米共轭：对所有的，，(1)从而定义了中的内积：对(2)注意，由(1)可见与不同。

Topological space, metric space, normed linear space and inner product space

在直角空间内建立了主从运动映射模型。

In Chapter 3, we discuss the other orthogonalities in in Banach space, and give some properties of them. The emphase of the chapter is to study the relations of Birkhoff orthogonality, Isosceles orthogonality and Pythagorean orthogonality, and it is proved that if one of these induces another, then the space is an inner product space.

第三章研究其它几种正交性问题，讨论Birkhoff正交性、Isosceles正交性与Pythagorean正交性之间的关系，证明了：如果这三种正交性的任一种都蕴含另一种，那么此空间就是内积空间。

Based on the minimizing vector theorem of the fuzzy inner product space ,the pseudo fuzzy orthogonal vector is defined and the projected theorem of the fuzzy inner product space is testified.

在模糊内积空间的极小化向量定理基础上，给出了向量拟模糊正交定义，并在模糊内积空间中证明了投影定理。

We paid special attention to the complex linear space consisting of all linear mappings from dimensional complex inner product space into dimensional complex inner product space .

2是与基的选择无关的概念。容易验证内积(2)满足内积的公理，从而是一个位的复内积空间。当是的正交归一基，是的正交归一基，可以证明构成的正交归一基。

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

To solve the problem, a knowledge aided space time adaptive processing scheme is presented, which incorporates knowledge sources of clutter with the general inner product nonhomogeneity detector in the secondary data selection of STAP.

该方法将待测距离单元杂波的先验知识与广义内积非同态检测器(general inner product nonhomogeneity detector， GIP NHD)结合，对训练样本进行有效选择。

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。