线性代数教与学过程中面临的问题

本文从线性代数教学实践出发,对线性代数教学过程中存在的问题进行了探讨和总结,以更好地开展线性代数课程教学方法的改革.     

浅谈将数学软件融入到线性代数教学中

本文指出了传统线性代数教学面临的问题,提出将数学软件融入到线性代数教学中,并简要列举了几例线性代数中的典型计算问题,从而有利于培养学生应用数学知识解决问题的能力。     

对经管、机电、土木类模块的线性代数课程改革与实践

本文给出了线性代数课堂教学模式的几种新形式,针对经管、机电、土木类模块提出线性代数课程的重要性,并通过线上教学补充线性代数课程内容,使之与专业相结合,为学生的后续学习打下良好的基础     

引入MATLAB进行线性代数教学的探究

分析了我国线性代数教学的现状,提出了在线性代数教学中结合MATLAB软件教学,并讨论题必要性,首先应用MATLAB在线性代数教学中可以使得抽象问题形象化;其次应用数学知识对实际问题进行建模通过数学软件使得求解变为可能;这些都以实际例子加以解释说明。最后提出结合Matlab进行线性代数教学以后的发展方向和存在的困难。     

独立学院线性代数中基于数学建模思想的案例教学探索

本文结合独立学院学生的学习特点以及线性代数的实践教学经验,努力将学科专业与线性代数理论教学内容相结合,基于数学建模思想的角度探索独立学院线性代数的案例教学的方法,旨在提高学生的创新能力以及分析、解决实际问题的能力。     

创新性线性代数课程的教学探究

针对线性代数教学现状,构建了以线性方程组为主线的、各章节紧密相关的创新性理论体系,并以行列式为案例,讲述了行列式的产生的知识背景、行列式的性质的几何解释,并以前后呼应的方式导出了Cramer法则,并把计算机软引入到实例分析当中,整个章节融合了创新思维和创新能力的培养,遵从了从理论到实践再到理论辩证规律。     

矩阵的秩在线性代数中的应用

矩阵的秩是线性代数中的一个重要研究工具和研究对象,以矩阵的秩作为主要研究对象,分析了矩阵的秩在线性代数中的一部分常见应用,对于学习和掌握线性代数有一定的帮助,进而加深对矩阵秩的理解,能灵活运用解决相关问题.     

MATLAB数学软件在线性代数教学中的应用

线性代数是高等院校工、管、理专业的一门重要基础课程,是用数学知识解决实际问题的一个强有力的工具。本文根据线性代数教学的特点,简单介绍了MATLAB数学软件,探讨了MATLAB在线性代数教学中的几点应用。     

浅谈线性代数的一些应用实例

给出了线性代数中多个知识点的应用实例,体现学以致用原则,激发学生的学习积极性,提高线性代数的教学效果。     

独立学院线性代数教学改革的探索

线性代数是理工科专业必修的一门基础课,该课程为学生学习专业知识提供必要的基础,具有较强的应用性,提高学生的抽象思维和逻辑思维能力。本文从提高学生学习线性代数的兴趣着眼,主要对独立学院线性代数的教学内容、教学方法及教学手段改革的探索。     

Matlab在线性代数教学中的应用研究

线性代数是工、管、理科各专业的数学必修课，是学生学习后续专业课的数学工具，同时也是研究生入学必考的科目。把Matlab应用到线性代数的教学中，在课堂上可以吸引同学们的注意力，激发学生学习本门课程的热情，提高教学效果。学生们在后续的专业课学习和工作中可以灵活使用线性代数这门数学工具。笔者结合课堂教学实践，举例说明Matlab在线性代数教学中的作用。     

高职院校线性代数教学研究

线性代数的教学内容看似比较简单,容易被教师所忽视,实际上高职院校的学生学习线性代数普遍都存在困难。文章主要从一些小问题入手探索高职院校线性代数的教学方法:打破常规,寻求变化,激励创新;注重过程,消除疑虑,记忆深刻;适当拓展,归纳总结,便于应用。     

Multilinear estimation of skewness and kutosis in linear models

Summary Estimation of the coefficients of skewness and kurtosis in a classical linear model situation is presented as an application of multilinear algebra and standard theory of mean estimation. The resulting estimators have optimality properties among all estimators that are invariant under mean translations, polynomials of degree three (skewness) or four (kurtosis) in the observations, and unbiased.     

Natural estimation of variances in a general finite discrete spectrum linear regression model

The method of “natural” estimation of variances in a general (orthogonal or nonorthogonal) finite discrete spectrum linear regression model of time series is suggested. Using geometrical language of the theory of projectors a form and properties of the estimators are investigated. Obtained results show that in describing the first and second moment properties of the new estimators the central role plays a matrix known in linear algebra as the Schur complement. Illustrative examples with particular regressors demonstrate direct applications of the results.     

A Dynamic Leontief Model with Non-renewable Resources

In this paper we study a generalization of the dynamic Leontief input–output model. We extend the standard dynamic Leontief model with the balance equation of non-renewable resources. Obviously, the non-renewable stocks will decrease, exploiting primary resources. In this study we examine the controllability of this extended model by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate how long these scarce resources will cover the input needs of production and how the lifetime of the system depends on the balanced growth rate and on the consumption. In doing so, we apply classic results from control theory and on eigenvalue problems in linear algebra.     

单层网壳极限承载力分析

文章采用线性屈曲、几何非线性及材料非线性和几何非线性耦合的分析方法,对某大跨度单层球面网壳进行极限承载力分析。分析表明,材料非线性对网壳结构的承载力均有较大的影响,采用线性屈曲、几何非线性分析方法均高估网壳结构的极限承载力,因此,要准确评估出网壳结构的极限承载力,就必须全面考虑网壳结构的几何非线性及材料非线性的影响。     

Polyhedral Combinatorics in Combinatorial Optimization

Polyhedral combinatorics is a subarea of combinatorial optimization of increasing practical importance. It deals with the application of the theory of linear systems and linear algebra to combinatorial problems. The paper is not intended as a survey on polyhedral combinatorics but it reviews some of the main concepts and proof techniques.     

The method of elimination and substitution in the GMM estimation of mixed regressive,spatial autoregressive models

This paper proposes a computationally simple GMM for the estimation of mixed regressive spatial autoregressive models. The proposed method explores the advantage of the method of elimination and substitution in linear algebra. The modified GMM approach reduces the joint (nonlinear) estimation of a complete vector of parameters into estimation of separate components. For the mixed regressive spatial autoregressive model, the nonlinear estimation is reduced to the estimation of the (single) spatial effect parameter. We identify situations under which the resulting estimator can be efficient relative to the joint GMM estimator where all the parameters are jointly estimated.     

First-order identification in linear models

The problem considered here is the ‘first-order’ identification of linear models, i.e., the identification of the coefficients of the variables appearing in the model. A general approach is proposed and very simple results are stated in this general context. A geometric interpretation of this approach is given. Classical results in this area are shown to be special cases of these general results.