{"id":21478418,"url":"https://github.com/mathworks-teaching-resources/applied-linear-algebra","last_synced_at":"2025-07-15T11:31:01.479Z","repository":{"id":199359277,"uuid":"702712109","full_name":"MathWorks-Teaching-Resources/Applied-Linear-Algebra","owner":"MathWorks-Teaching-Resources","description":"A collection of teaching scripts showing applications of linear algebra to chemistry, computer science, mechanical engineering, and more.","archived":false,"fork":false,"pushed_at":"2024-08-23T22:14:35.000Z","size":53363,"stargazers_count":13,"open_issues_count":0,"forks_count":3,"subscribers_count":3,"default_branch":"release","last_synced_at":"2024-08-23T23:28:30.930Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"MATLAB","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"bsd-3-clause","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/MathWorks-Teaching-Resources.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE.md","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":"SECURITY.md","support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2023-10-09T21:19:57.000Z","updated_at":"2024-08-23T23:28:33.740Z","dependencies_parsed_at":null,"dependency_job_id":"68b8b8b3-5be9-4b69-8830-73863021a0fd","html_url":"https://github.com/MathWorks-Teaching-Resources/Applied-Linear-Algebra","commit_stats":null,"previous_names":["mathworks-teaching-resources/applied-linear-algebra"],"tags_count":5,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/MathWorks-Teaching-Resources%2FApplied-Linear-Algebra","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/MathWorks-Teaching-Resources%2FApplied-Linear-Algebra/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/MathWorks-Teaching-Resources%2FApplied-Linear-Algebra/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/MathWorks-Teaching-Resources%2FApplied-Linear-Algebra/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/MathWorks-Teaching-Resources","download_url":"https://codeload.github.com/MathWorks-Teaching-Resources/Applied-Linear-Algebra/tar.gz/refs/heads/release","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":226033480,"owners_count":17563169,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-11-23T11:18:16.420Z","updated_at":"2024-11-23T11:18:17.341Z","avatar_url":"https://github.com/MathWorks-Teaching-Resources.png","language":"MATLAB","funding_links":[],"categories":[],"sub_categories":[],"readme":"\n# \u003cspan style=\"color:rgb(213,80,0)\"\u003eApplied Linear Algebra\u003c/span\u003e\n\n\n[![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/136364-applied-linear-algebra) or [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=README.mlx)\n\n[![MATLAB Versions Tested](https://img.shields.io/endpoint?url=https%3A%2F%2Fraw.githubusercontent.com%2FMathWorks-Teaching-Resources%2FApplied-Linear-Algebra%2Frelease%2FImages%2FTestedWith.json)](https://MathWorks-Teaching-Resources.github.io/Applied-Linear-Algebra)\n\n**Curriculum Module**\n\n_Created with R2024a. Compatible with R2024a and later releases._\n\n# Information\n\nThis curriculum module contains interactive [MATLAB® live scripts](https://www.mathworks.com/products/matlab/live-editor.html) that apply fundamental concepts and basic terminology related to linear algebra. There is a focus on identifying applications of linear algebra to academic disciplines beyond mathematics.\n\n\n## Background\n\nYou can use this live script as demonstrations in lectures, class activities, or interactive assignments outside class. Applied Linear Algebra covers topics from a first course in linear algebra including vector and matrix arithmetic, solving matrix equations, null spaces, eigenvalues, and eigenvectors. Applications include balancing chemical reactions, solving static force scenarios, encryption, systems modeling, and explainable machine learning.\n\n\nThe 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 \u003cimg src=\"Images/EndIcon.png\" width=\"19\" alt=\"EndIcon.png\"\u003e Stop button in the **RUN** section of the **Live Editor** tab in the MATLAB Toolstrip.\n\n## Contact Us\n\nSolutions are available upon instructor request. Contact the [MathWorks online teaching team](mailto:onlineteaching@mathworks.com) if you would like to request solutions or have a question.\n\n\n## Prerequisites\n\nThese scripts assume knowledge of basic linear algebra such as vectors, matrices, eigenvalues, and eigenvectors, as discussed in the related courseware on matrix methods. The focus of these scripts is on reinforcing the theoretical knowledge of linear algebra concepts by applying them in a variety of domains. There is minimal MATLAB knowledge required for these scripts, but you could use [MATLAB Onramp](https://matlabacademy.mathworks.com/details/matlab-onramp/gettingstarted) as a resource to acquire familiarity with live scripts and MATLAB syntax.\n\n\n# Getting Started \n## Accessing the Module\n### **On MATLAB Online:**\n\nUse the [\u003cimg src=\"Images/OpenInMO.png\" width=\"136\" alt=\"OpenInMO.png\"\u003e](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj) link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see an app with several navigation options to get you started.\n\n### **On Desktop:**\n\nDownload or clone this repository. Open MATLAB, navigate to the folder containing these scripts and double\\-click on [AppliedLinAlg.prj](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=README.mlx). It will add the appropriate files to your MATLAB path and open an app that asks you where you would like to start. \n\n\nEnsure you have all the required products (listed below) installed. If you need to include a product, add it using the Add\\-On Explorer. To install an add\\-on, go to the **Home** tab and select  \u003cimg src=\"Images/AddOnsIcon.png\" width=\"16\" alt=\"AddOnsIcon.png\"\u003e **Add-Ons** \u003e **Get Add-Ons**. \n\n## **Working through the module:**\n1.  In the opening app, select \"Main Menu\" to open a brief hyperlinked navigation page or \"README\" to open this page. To give us feedback, select \"Feedback\".\n2. Get started with each topic by clicking the link to open the live script. The instructions inside each live script will walk you through the live script and related functions.\n\n## Products\n\nMATLAB® is used throughout. Tools from the Symbolic Math Toolbox™ are used frequently as well. The \u003csamp\u003esevilla.jpg\u003c/samp\u003e image in \u003csamp\u003eSteganography.mlx\u003c/samp\u003e comes from the Image Processing Toolbox™. The \u003csamp\u003eIdentifyDigits\u003c/samp\u003e and \u003csamp\u003eReadMyWriting\u003c/samp\u003e scripts use both the Image Processing Toolbox™, and the Statistics and Machine Learning Toolbox™. \u003csamp\u003eIdentifyDigits\u003c/samp\u003e also uses the Deep Learning Toolbox™ while \u003csamp\u003eReadMyWriting\u003c/samp\u003e uses MATLAB Mobile.\n\n# Scripts\n## [BalancingChemicalEquations](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=Scripts/BalancingChemicalEquations.mlx)\n|      |      |      |\n| :-- | :-- | :-- |\n| Chemical reactions \u003cbr\u003e  | **In this script, students will...** \u003cbr\u003e  | **Academic disciplines** \u003cbr\u003e   |\n| \u003cimg src=\"Images/Reaction.png\" width=\"171\" alt=\"Reaction.png\"\u003e \u003cbr\u003e  | • build and solve matrix equations \u003cbr\u003e • identify the rank and null spaces of matrices \u003cbr\u003e • balance chemical reactions \u003cbr\u003e  | • Chemistry \u003cbr\u003e • Mathematics \u003cbr\u003e   |\n|      |      |       |\n\n## [MarkovModeling](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=Scripts/MarkovModeling.mlx)\n|      |      |      |\n| :-- | :-- | :-- |\n| Zombie outbreak \u003cbr\u003e  | **In this script, students will...** \u003cbr\u003e  | **Academic disciplines** \u003cbr\u003e   |\n| \u003cimg src=\"Images/SIZ-diagram-complete.png\" width=\"171\" alt=\"SIZ-diagram-complete.png\"\u003e \u003cbr\u003e  | • compute powers of transition matrices \u003cbr\u003e • compute eigenvalues and eigenvectors and explain their meaning in a modeling context \u003cbr\u003e • create a model of a zombie outbreak \u003cbr\u003e • analyze real\\-world scenarios for mayflies and HIV \u003cbr\u003e  | • Biology \u003cbr\u003e • Mathematics \u003cbr\u003e   |\n|      |      |       |\n\n## [Steganography](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=Scripts/Steganography.mlx)\n|      |      |      |\n| :-- | :-- | :-- |\n| Image encryption \u003cbr\u003e  | **In this script, students will...** \u003cbr\u003e  | **Academic disciplines** \u003cbr\u003e   |\n| \u003cimg src=\"Images/SmStorm.png\" width=\"171\" alt=\"SmStorm.png\"\u003e \u003cbr\u003e  | • use matrix arithmetic \u003cbr\u003e • represent images and text as matrices \u003cbr\u003e • encrypt images inside other images \u003cbr\u003e  | • Computer Science \u003cbr\u003e • Mathematics \u003cbr\u003e   |\n|      |      |       |\n\n## [StaticForces](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=Scripts/StaticForces.mlx) and [Moments](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=Scripts/Moments.mlx)\n|      |      |      |\n| :-- | :-- | :-- |\n| Static force analysis \u003cbr\u003e  | **In these scripts, students will...** \u003cbr\u003e  | **Academic disciplines** \u003cbr\u003e   |\n| \u003cimg src=\"Images/SupportedDoor.png\" width=\"171\" alt=\"SupportedDoor.png\"\u003e \u003cbr\u003e  | • define and normalize vectors \u003cbr\u003e • build and solve matrix equations \u003cbr\u003e • calculate dot products and cross products \u003cbr\u003e • solve for moments, tensions, and forces \u003cbr\u003e  | • Civil Engineering \u003cbr\u003e • Mechanical Engineering \u003cbr\u003e • Mathematics \u003cbr\u003e   |\n|      |      |       |\n\n## [Identify Digits](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=Scripts/IdentifyDigits.mlx) and [ReadMyWriting](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=Scripts/ReadMyWriting.mlx)\n|      |      |      |\n| :-- | :-- | :-- |\n| Machine learning \u003cbr\u003e  | **In these scripts, students will...** \u003cbr\u003e  | **Academic disciplines** \u003cbr\u003e   |\n| \u003cimg src=\"Images/ConfusionMatrix.png\" width=\"171\" alt=\"ConfusionMatrix.png\"\u003e \u003cbr\u003e  | • use singular value decomposition and distance \u003cbr\u003e • use binary morphology tools to preprocess image data \u003cbr\u003e • create a tool that will identify handwritten digits \u003cbr\u003e  | • Computer Science \u003cbr\u003e • Mathematics \u003cbr\u003e   |\n|      |      |       |\n\n## [Robotics](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-Linear-Algebra\u0026project=AppliedLinAlg.prj\u0026file=Scripts/Robotics.mlx)\n|      |      |      |\n| :-- | :-- | :-- |\n| Robotic manipulators \u003cbr\u003e  | **In this script, students will...** \u003cbr\u003e  | **Academic disciplines** \u003cbr\u003e   |\n| \u003cimg src=\"Images/RoboticArm.png\" width=\"171\" alt=\"RoboticArm.png\"\u003e \u003cbr\u003e  | • compute the Cartesian result of a sum of polar vectors \u003cbr\u003e • explore the concept of a configuration space through visualizations \u003cbr\u003e • explain the connection between degrees of freedom, multiplicity of solutions, and the null space \u003cbr\u003e  | • Mechanical engineering \u003cbr\u003e • Mathematics \u003cbr\u003e   |\n|      |      |       |\n\n# License\n\nThe license for this module is available in the [LICENSE.md](https://github.com/MathWorks-Teaching-Resources/Applied-Linear-Algebra/blob/release/LICENSE.md).\n\n# Related Courseware Modules\n-  [Matrix Methods of Linear Algebra](https://github.com/MathWorks-Teaching-Resources/Matrix-Methods-of-Linear-Algebra) is available on [GitHub](https://github.com/MathWorks-Teaching-Resources/Matrix-Methods-of-Linear-Algebra) or [\u003cimg src=\"Images/OpenInFX.png\" width=\"104\" alt=\"OpenInFX.png\"\u003e](https://www.mathworks.com/matlabcentral/fileexchange/94730-matrix-methods-of-linear-algebra) or [\u003cimg src=\"Images/OpenInMO.png\" width=\"136\" alt=\"OpenInMO.png\"\u003e](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Matrix-Methods-of-Linear-Algebra\u0026project=MatrixMethods.prj) \n-  [Vector Arithmetic](https://github.com/MathWorks-Teaching-Resources/Vector-Arithmetic) is available on [GitHub](https://github.com/MathWorks-Teaching-Resources/Vector-Arithmetic) or [\u003cimg src=\"Images/OpenInFX.png\" width=\"104\" alt=\"OpenInFX.png\"\u003e](https://www.mathworks.com/matlabcentral/fileexchange/94555-vector-arithmetic) or [\u003cimg src=\"Images/OpenInMO.png\" width=\"136\" alt=\"OpenInMO.png\"\u003e](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Vector-Arithmetic\u0026file=vectorBasics.mlx) \n\nOr feel free to explore our other [modular courseware content](https://www.mathworks.com/matlabcentral/fileexchange/?q=tag%3A%22courseware+module%22\u0026sort=downloads_desc_30d).\n\n# Educator Resources\n-  [Educator Page](https://www.mathworks.com/academia/educators.html) \n\n# Contribute \n\nLooking for more? Find an issue? Have a suggestion? Please contact the [MathWorks teaching resources team](mailto:%20onlineteaching@mathworks.com). If you want to contribute directly to this project, you can find information about how to do so in the [CONTRIBUTING.md](https://github.com/MathWorks-Teaching-Resources/Applied-Linear-Algebra/blob/release/CONTRIBUTING.md) page on GitHub.\n\n\n© *Copyright 2023 The MathWorks, Inc.*\n\n\r\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmathworks-teaching-resources%2Fapplied-linear-algebra","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmathworks-teaching-resources%2Fapplied-linear-algebra","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmathworks-teaching-resources%2Fapplied-linear-algebra/lists"}