线性代数入门常用的基本矩阵方法

本课程模块包含交互式实况脚本，用于教授线性代数入门课程中常用的基本矩阵方法。在每个实况脚本的第一部分，学生学习标准定义、可视化概念并在纸上进行练习。之后，学生练习互补的MATLAB方法。这些方法强化了讨论的概念，帮助学生尽早熟悉计算软件。每节课都以一个示例性应用程序结束。这些实况脚本可以用作讲座的一部分，作为教学环境中的活动，或作为课外完成的交互式作业。

This curriculum module contains interactive live scripts that teach fundamental matrix methods commonly taught in introductory linear algebra courses. In the first part of each live script, students learn standard definitions, visualize concepts, and perform exercises on paper. Afterward, students practice complementary MATLAB methods. These methods reinforce the discussed concepts and help students to develop an early familiarity with computational software. Each lesson concludes with an illustrative application. These live scripts can be used as part of a lecture, as activities in an instructional setting, or as an interactive assignment to be completed outside of class.

The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.

Get started with the interactive examples

Option 1: Download to Desktop Download and unzip the repository. Then, double-click the MatrixMethods.prj file inside MATLAB.

Option 2: Open in MATLAB Online Log in to your MathWorks account to access your license. If you are associated with a university, use your university email to access a license.

From there, you can follow the landing page instructions to get started with the examples.

The instructions inside the live scripts will guide you through the exercises and activities.

Get started with each live script by running it one section at a time.

To stop running the script or a section midway (for example, if a loop is running longer than intended), click the  Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.

Details

matrixOperations.mlx, matrixOperationsSoln.mlx
An interactive lesson that explores basic matrix operations.

Learning Goals:

Define matrices and their basic arithmetic operations

Calculate the result of matrix operations on paper and in MATLAB

Explain the size requirements of matrix operations

Compare symbolic and numeric matrix operations in MATLAB

Apply matrix methods to modify grayscale images

linearSystems.mlx, linearSystemsApplications.mlx, linearSystemsSoln.mlx, linearSystemsApplicationsSoln.mlx
An interactive lesson that explores matrix representations of linear systems and their solutions.

Learning Goals:

Write a linear system in matrix form

Relate solutions of linear systems in 3-dimensions to their visualizations

Solve systems of linear equations using row-reduction

Solve systems of linear equations using matrix inverses

Explain the solvability of a linear system in terms of the matrix determinant

Use MATLAB to solve linear systems

Apply matrix methods to linear regression and linear circuit analysis

eigenanalysis.mlx, eigenanalysisApplications.mlx, eigenanalysisSoln.mlx, eigenanalysisApplicationsSoln.mlx
An interactive lesson that explores eigenvectors, eigenvalues, and their applications.

Learning Goals:

Visualize eigenvectors in 2-dimensions

Solve for the eigenvalues and eigenvectors of a 2x2 matrix on paper and larger matrices using MATLAB

Diagonalize 2x2 matrices on paper and larger matrices in MATLAB

Explain linear system solvability in terms of eigenvalues

Discuss defective matrices

Use eigenanalysis to understand vibrations and the long term behavior of a Markov chain

Products

MATLAB, Symbolic Math Toolbox, Image Processing Toolbox, Statistics and Machine Learning Toolbox

License

The license for this module is available in the LICENSE.TXT file in this GitHub repository.

Educator Resources

Featured Courseware

Teach with MATLAB and Simulink

MATLAB Grader

编辑：黄飞