{"id":23161731,"url":"https://github.com/farbodbj/linear_algebra_1401","last_synced_at":"2025-04-04T19:37:25.710Z","repository":{"id":176150114,"uuid":"655068519","full_name":"farbodbj/Linear_Algebra_1401","owner":"farbodbj","description":"assignments of linear algebra course in AUT-CE in year 2023","archived":false,"fork":false,"pushed_at":"2023-06-17T19:52:11.000Z","size":4054,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-02-10T04:31:53.001Z","etag":null,"topics":["linear-algebra","numpy","python"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/farbodbj.png","metadata":{"files":{"readme":"README.MD","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2023-06-17T19:33:54.000Z","updated_at":"2023-07-12T12:46:34.000Z","dependencies_parsed_at":null,"dependency_job_id":"49b0f1ec-33a6-4332-885b-fde961e3557f","html_url":"https://github.com/farbodbj/Linear_Algebra_1401","commit_stats":null,"previous_names":["farbodbj/linear_algebra_1401"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/farbodbj%2FLinear_Algebra_1401","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/farbodbj%2FLinear_Algebra_1401/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/farbodbj%2FLinear_Algebra_1401/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/farbodbj%2FLinear_Algebra_1401/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/farbodbj","download_url":"https://codeload.github.com/farbodbj/Linear_Algebra_1401/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":247238601,"owners_count":20906470,"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":["linear-algebra","numpy","python"],"created_at":"2024-12-17T23:15:19.711Z","updated_at":"2025-04-04T19:37:25.696Z","avatar_url":"https://github.com/farbodbj.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"\n# Linear Algebra Homeworks\n\nThis repository contains my homework assignments for the Linear Algebra course taught by [Professor Maryam Amir Mazlaghani](https://scholar.google.com/citations?user=gxbTUfEAAAAJ\u0026hl=en) at Amirkabir University of Technology. The assignments are focused on practical applications of linear algebra concepts and all the implementations has been done in python and using numpy library.\n## Homework Descriptions\n### Homework 1: Gaussian Elimination and Row Operations\nIn this assignment, I implemented algorithms for solving linear systems using Gaussian elimination and row operations. The Python code takes in a matrix as input and returns the solution to the system of equations. The implementation is based on the algorithm provided in the textbook.\n### Homework 2: Transpose and Determinant Functions\n\nIn this assignment, I explored the practical uses of transpose and determinant functions in linear algebra. The Python code calculates the transpose and determinant of a given matrix and tries to maximize the determinant of a special type of matrices (provided in the exercise).\n### Homework 3: Error Detection and Correction with Hamming Code\n\nIn this assignment, I implemented the Hamming code method to detect and correct errors in digital data transmission. The Python code generates error-correcting codes and demonstrates how to detect and correct bit errors.\n### Homework 4: Power Method, Inverse Power Method, QR Factorization, and Gram-Schmidt Algorithm\n\nIn this assignment, I implemented algorithms for finding the dominant eigenvalue and eigenvector of a matrix using the power method and inverse power method. I also implemented the QR factorization and Gram-Schmidt algorithms to find an orthonormal basis for the column space of a matrix which were co-related. The Python code includes test cases for each algorithm which are relatively large matrices. The correctness is being tested using numpy's in-built testing functionalities.\n### Homework 5: SVD and Dimension Reduction\n\nIn this assignment, I used Singular Value Decomposition (SVD) to perform dimension reduction on a dataset of food data (NNDB dataset). The Python code first reads and pre-proccess the data as a pandas dataframe and then  reduces the dimensionality of the dataset using SVD and other formulas and reports the error after the reduction. The data is also visualized using Matplotlib.\n\n## Note\nPlease note that my code is not error-free and may not always work perfectly. I have implemented some functions in numpy or other Python packages by myself for learning purposes.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ffarbodbj%2Flinear_algebra_1401","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ffarbodbj%2Flinear_algebra_1401","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ffarbodbj%2Flinear_algebra_1401/lists"}