线性结合代数

词组短语

linear associative algebra

与线性结合代数相关的网络例句 [注：此内容来源于网络，仅供参考]

Linear Algebra is mainly a subject which studies the linear structure of finite dimensional linear space and its linear transformation while linear concept is in itself from the old Euclid Geometry. The concept of "Linear Space" is a kind of algebraic abstract. In many fields of modern engineering project and technology, because of the influence of computer and graph showing, the algebraic disposal of geometric questions, the visual disposal of algebraic questions, algebra and geometry are tightly combined.

线性代数主要是研究有限维线性空间及其线性变换这一代数结构的学科，而线性概念究其根源则是来自古老的Euclid几何，线性空间概念是几何空间的一种代数抽象，在现代工程技术的许多领域里，由于计算机及图形显示的强大威力，几何问题的代数化处理，代数问题的可视化处理，把代数与几何更加紧密地结合在一起。

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

As an example of the application of some knowledge of Linear Algebra,this paper discusses the application of an invertible matrix in secure communication,some basic problems of this application,and the solutions to these problems.

作为工科"线性代数"课中相关知识的一个具体应用的例子，从理论与实践相结合的角度论述了可逆矩阵在保密通信中的应用及其存在的问题与对策等。

In the research to demand of International reserves,first, according to the affective character of demand to transition of International reserves, choosing the decision theory of Markov and dynamic transition equation as basic model, the paper has set up two transition methods--- stationary matrix and dynamic matrix, the later matrix has improved the sensitive reaction to time and velocity. Second, combining with knowledge of linear algebra, the paper has analyzed and testified the positive associated relation between transition matrix elements on main diagonal and the convergent speed of system, and explained why international reserves transition embodies the character under new situation and why the transition process can be accelerated by the strike of international idle money. Third,on the quantitative calculating to elements of transition matrix,referring to multiplication theory and decomposing-composing method of system, the paper has transformed main three-factor deciding confidence of international monetary into detail modulus by comparing analysis measure,now the matrix has been decided.

在国际储备的需求分析研究中，本文首先选择马尔可夫转移方程作为基础模型，根据需求对外汇储备结构的影响特点，提出非定常转移矩阵变换方法，拓展了马尔可夫变换对时间和速度的敏感性；结合线性代数知识，分析证明了定常转移矩阵的主对角线元素值的大小与系统的收敛速度的正向关联关系，并利用结论解释了国际货币新动向下外汇储备转换表现出的趋势特点以及国际游资冲击对国际货币结构变化的加速影响；在转移矩阵元素的量化计算上，本文参考乘数理论和系统分解合成原理，采用对比分析方法把影响国际货币信心的三大要素综合量化为转移偏好系数，然后根据转移偏好系数确定转移矩阵的元素值，其中还分别具体给出了定常转移矩阵和非定常转移矩阵的计算方法及在变换中的使用方法，从而不仅在定量分析上应证了定性分析结论，而且反映了随时间变化的美圆、欧元、日圆的比例结构均衡过程。

Then we apply it to a C-module V, where V is a n-dimensional vector space and the operator from C×V to V is defined by a linear transformation T of V, then we get a unique factorization of V and a right basis under which the transformation matrix of T is T's Jordan canonical form.

然后把它应用到一个具体的C-模V，其中V是n维线性空间，C×V到V的映射由V中的一个线性变换T定义，从而得到V的一个唯一分解，再结合线性代数有关知识给出V的一组基，T在这组基下的变换矩阵恰为T的Jordan标准形。

This paper, based on the secong approach, presents a new efficient algorithm to design symmetric bi-orthogonal M-band wavelets with arbitrary regularity by using Grobner basis and syzygy module algorithm in computing algebra, which bi-orthogonalizes the polyphase matrix line by line.

本文基于第二种思路结合计算代数中Groebner基和合冲模的思想和算法提出了一种同时具有任意正则阶和线性相位性质的M带双正交小波的新型高效构造算法，其中采用多相位矩阵逐行双正交化的方法。

Elastic and inelastic differential and integral cross sections for low-energy vibrational excitation of H2 by electron impact are studied with exact exchange. The resulting coupled integrodifferential equations are solved using a combination of linear-algebraic and R-matrix-propagator techniques.

严格交换势用于研究低能电子与H2分子的弹性和非弹性散射截面，线性代数方法和R-矩阵传播子相结合求解基于振动密耦合方法的积分-微分耦合方程组，由此得到收敛的散射微分截面和积分截面。

As an example of the application of some knowledge of Linear Algebra,this paper discusses the application of an invertible matrix in secure communication,some basic problems of this application,and the solutions to these problems.

作为工科&线性代数&课中相关知识的一个具体应用的例子，从理论与实践相结合的角度论述了可逆矩阵在保密通信中的应用及其存在的问题与对策等。

C.R.Miers has shown that the Lie triple derivation on a vN algebra M with no central abelian summands has the form D +λ, where D is an associative derivation and A is a linear map of M into its center which annihilates brackets of operators.

Miers证明了无交换部分的vN代数M上的三元Lie导子具有D+λ形式，其中D是M上的结合导子，λ是从M到它的中心Z上的线性映射且零化M中的括积。

与线性结合代数相关的网络解释 [注：此内容来源于网络，仅供参考]

Albert：阿尔贝特

在证明中他们使用了类域论方面的重要定理--格伦瓦尔德定理. 这个猜想的证明,在当时的数学界是一件大事. 美国著名代数学家A.A.阿尔贝特(Albert)说:线性结合代数的理论,当决定所有有理可除代数的问题找到了解答的时候,也

linear associative algebra：线性结合代数

1870年,Peirce 还出版了>(Linear Associative Algebra);这是第一部美国产有水准的纯数学著作,它在1881年开始受到欧洲数学家的重视. Peirce 受到的是本土教育,学到的是法国的数学与物理,从事过应用数学的工作,着手过数学教育的改革,

linear approximation problem：线性逼近问题

linear approximation 线性近似 | linear approximation problem 线性逼近问题 | linear associative algebra 线性结合代数

linear closure：线性闭包

linear associative algebra 线性结合代数 | linear closure 线性闭包 | linear combination 线性组合

vector space：向量空间

一个重要概念是向量(vector),广义地称为向量空间(vector space). 这些属于线性代数(linear algebra)的研究范畴. 向量研究把数量、结构和空间三个方面结合起来. 而向量微积分(vector calculus)将研究拓展到另一个领域,即变化.