内积空间

Linear algebra (2) studies the structure, including the inner product, angle, and projection, of the Euclidean space .

线性代数介绍欧几里德空间的结构，包括内积、角度、投影等。

In this paper,quadratic form theory,the European space inner product nature and Jensen inequality are three ways to prove cauchy inequality,and bthe relation between Cauchy inequality and higher mathematics was illustrated briefly.

本文运用二次型理论、欧式空间中内积性质和詹森不等式三种方法证明柯西不等式，并简要说明柯西不等式与高等数学之间的联系。

The notion of a complete random inner product module is a random generalization of that of a Hilbert space.

完备随机内积模是Hilbert 空间的随机推广。

Firstly, this paper introduces a function space defined by Bouziani and takes the inner product in space L2 of the linear equation and an integrodifferential operator.

首先引入一个Bouziani定义的空间，利用该空间的一些特点，将原线性方程的两端在L~2空间内与一个积分微分算子作内积。

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。

According to the inner product feature of sample space this paper takes the differential of fast changing parameters into input samples and puts forward a new neural network not to require to iterate learn, taking it for example recording data of the record system of a type of aeroengine and taking out identification to it.

根据样本空间的内积特性，在输入样本中引入快变参数的导数项，提出了一种无需迭代学习的内积神经网络。

In this approach, the integral operator kernel functions is used to realize the nonlinear map from the raw feature space of gear vibration signals to high dimensional feature space.

该方法通过计算齿轮振动信号原始特征空间的内积核函数来实现原始特征空间到高维特征空间的非线性映射。

The integral operator kernel functions is used to realize the nonlinear map from the raw feature space of gear vibration signals to high dimensional feature space.

该方法通过计算齿轮振动信号原始特征空间的内积核函数来实现原始特征空间到高维特征空间的非线性映射。

Recently , the classical Riesz representation theorem on Hilbert spaces has been generalized onto complete random inner product modules ,in this paper the classical Friedrichs theorem on Hilbert spaces is generalized onto complete random inner product modules.

最近，经典的Riesz 表示定理已经被推广到完备随机内积模上，在此基础上本文将Hilbert 空间上经典的Friedrichs 定理推广到完备随机内积模上。首先，证明完备随机内积模上任一正Her2 mite 型惟一地对应一个正自共轭算子。

This method is tectonic on foundation of nuclear function theory special and linear space, each issue of rank nucleus of progression of the Volterra that seek solution changeover uses output observation vector to be in to beg Xierbaite the some in the space child the umbriferous problem on the space, make originally complex, hard calculative is nonlinear in the approachs a problem to be built in place compose linear space of Volterra progression of the system solve ably with the means that accumulates inside vector, gave out specific algorithm.

该方法在核函数理论基础上构造非凡线性空间，将求解Volterra级数的各阶核的新问题转换为求用输出观测向量在希尔伯特空间中某一子空间上的投影新问题，使原本复杂、难以计算的非线性系统的Volterra级数的逼近新问题在所构建的线性空间中巧妙地以向量内积的方式解决，并给出了具体算法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。