This repository contains projects related to Linear Algebra, completed as part of academic coursework and teaching assistant activities in the Linear Algebra course at the University of Tehran. It includes one project completed as a student and two additional projects designed and implemented as a teaching assistant, demonstrating a range of linear algebra applications in both theoretical and practical contexts.
Implemented by: Erfan Asgari, Sina Mohammadi
Students of Linear Algebra | Spring 2023 | Dr. Yazdanpanah | University of Tehran
This project focuses on SVD-based image watermarking techniques for multimedia protection. Using Singular Value Decomposition (SVD), the goal is to embed watermarks in a way that resists unauthorized tampering while maintaining high imperceptibility. The project explores a SVD-based watermarking scheme, its robustness, and its effectiveness in preserving intellectual property.
Keywords: SVD, Watermarking, Singular Value Decomposition, Multimedia Security, Robustness
Designed by: Erfan Asgari, Fardin Abbasi
Teaching Assistants of Linear Algebra | Spring 2024 | Dr. Sarafraz | University of Tehran
This project introduces students to Markov chains and numerical methods in linear algebra. It covers the analysis of Markov matrices, eigenvalues, and eigenvectors, with a specific application to Economics for business cycle analysis. The project demonstrates how these mathematical tools can help analyze economic trends and improve policy making.
Keywords: Markov Chains, Business Cycle, Linear Algebra, Eigenvalue, Numerical Methods, Monte Carlo
Designed by: Erfan Asgari, Fardin Abbasi
Teaching Assistants of Linear Algebra | Spring 2024 | Dr. Sarafraz | University of Tehran
This project applies Latent Semantic Analysis (LSA) to classify news articles into five categories. It involves text preprocessing, Bag of Words, TF-IDF, and using truncated SVD. The implementation includes a detailed analysis of word embeddings and classification based on semantic similarities.
Keywords: Latent Semantic Analysis, Truncated SVD, NLP, Text Classification, Cosine Similarity, Word Embeddings