内积

A vector inner product space defined by covariance is introduced in the above study, which greatly ease the theoretical analyst of principle and performance of image fusion methods.

在这一过程中引入了一种以协方差定义的图像向量内积空间，极大的简化了对融合原理和融合性能的分析。

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。

This method transforms the discrete problem to continuous function space and convert the inner product computation problem in Hilbert space into function evaluation problem in some discrete points.

该方法将离散的问题影射到连续函数空间中进行处理，同时将Hilbert空间中的内积计算问题转化为函数在离散点的取值问题。

In this paper,it is proved that a Minkowski plane with π/2-property,whose unit circle is Radon curve,is an inner product space .

证明了单位圆是Radon曲线，且具有π/2性质的M inkowski平面，是内积空间

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。

The topics are divided into eight chapters and two appendices, is to learn from the preamble of Chapter 1 to Chapter 7 of the preparation of knowledge, that is, inner product space Chapter 1 on the basis of Fourier series of knowledge Chapter 2 on Fourier Transform Chapter 3 introduced the Discrete Fourier Transform and Fast Fourier Transform Chapter 4 to Chapter 7 to discuss wavelet, with emphasis on construction of orthogonal wavelet appendix describes slightly complex themes, as well as a number of technical concepts or produce demo MATLAB graphics code

全书分为8章和2个附录，前言部分是学习第1章至第7章的准备知识，即内积空间；第1章讲解傅里叶系列的基础知识；第2章讲解傅里叶变换；第3章介绍离散傅里叶变换以及快速傅里叶变换；第4章至第7章讨论小波，重点在于正交小波的构建；附录部分则介绍稍微复杂的一些技术主题以及演示概念或产生图形的MATLAB代码。

At last, the Double Message Signal is proposed and the non-interfere condition is presented that the steering vectors are orthogonal in the weighted inner product space, with the inverse matrix of background covariance as the weighting matrix. The optimal polarization states are designed, according to the EM background.

最后，提出了一种双信息信号传输的方案并导出了无互扰传输的充要条件：两期望信号的信号矢量在以干扰噪声协方差矩阵的逆矩阵为加权矩阵的加权内积空间中正交，在给定的电磁环境下设计了双信息信号的极化状态。

We first analyze the relationship between the characteris-tic subspaces of linear transformation A,and its conjuge transformation A*, on then-dimensional complex inner product space Cn, and prove that the characteristicsubspace of an enginvalueλof A is orthogonal to that of enginvalue μ of A* if λ≠μ.

首先，分析n-维复内积空间Cn上的线性变换A与其共轭变换A*的特征子空间之间的关系，证明出只要A的一个特征值λ与A*的一个特征值μ的共轭不同，那么它们对应的特征子空间是正交的。

If the knowledge was closely related the many disciplines or many branches of a discipline,then this knowledge is certainly important,but the quadratic form,european space inner product,Jensen inequality are basic content of algebra,real letters,calculus in higher mathematics.

如果某一知识跟很多学科或者一个学科的很多分支有着密切联系，那么这个知识肯定是很重要的，而二次型、欧式空间内积、詹森不等式都是高等数学中代数、实函、微积分的基本内容。

Reproducing kernel Hilbert space ; inner product ; orthonormal basis

再生核Hilbert空间；内积；正交基

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。