{"id":25343578,"url":"https://github.com/saadsalmanakram/matrix-singularity-and-cipher","last_synced_at":"2025-04-08T14:27:29.729Z","repository":{"id":274692055,"uuid":"846265020","full_name":"saadsalmanakram/Matrix-Singularity-and-Cipher","owner":"saadsalmanakram","description":"My love triangle. Your complete guide to Maths, Physics And Computer...","archived":false,"fork":false,"pushed_at":"2025-01-28T19:36:47.000Z","size":3,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-02-14T10:50:12.245Z","etag":null,"topics":["computing","mathematical-programming","mathematics","physics"],"latest_commit_sha":null,"homepage":"","language":null,"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/saadsalmanakram.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":"2024-08-22T21:10:59.000Z","updated_at":"2025-01-28T19:36:50.000Z","dependencies_parsed_at":"2025-01-28T20:41:40.840Z","dependency_job_id":null,"html_url":"https://github.com/saadsalmanakram/Matrix-Singularity-and-Cipher","commit_stats":null,"previous_names":["saadsalmanakram/matrix-singularity-and-cipher"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/saadsalmanakram%2FMatrix-Singularity-and-Cipher","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/saadsalmanakram%2FMatrix-Singularity-and-Cipher/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/saadsalmanakram%2FMatrix-Singularity-and-Cipher/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/saadsalmanakram%2FMatrix-Singularity-and-Cipher/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/saadsalmanakram","download_url":"https://codeload.github.com/saadsalmanakram/Matrix-Singularity-and-Cipher/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":247859466,"owners_count":21008108,"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":["computing","mathematical-programming","mathematics","physics"],"created_at":"2025-02-14T10:39:35.606Z","updated_at":"2025-04-08T14:27:29.498Z","avatar_url":"https://github.com/saadsalmanakram.png","language":null,"funding_links":[],"categories":[],"sub_categories":[],"readme":"\n---\n\n# 📊 Matrix, Singularity, and Cipher – The Ultimate Guide to Mathematics, Physics, and Computing  \n\n![Mathematics \u0026 Physics](https://cdn.pixabay.com/photo/2024/06/22/18/16/ai-generated-8846765_1280.png)  \n## 📌 Introduction  \n\nMathematics, Physics, and Computing are the **fundamental pillars** of modern science and technology. This repository serves as a **comprehensive guide** to understanding advanced topics in **Linear Algebra, Calculus, Quantum Mechanics, Cryptography, and Computational Mathematics**.  \n\n📌 **Learn the foundations of Pure and Applied Mathematics**  \n📌 **Understand key concepts in Physics, including Quantum Mechanics and Relativity**  \n📌 **Explore the relationship between Mathematics, Algorithms, and Computing**  \n📌 **Delve into Cryptography and Secure Communication Techniques**  \n\n---\n\n## 🚀 Features  \n\n- 📖 **Linear Algebra, Calculus, and Differential Equations**  \n- 🔥 **Physics Topics: Quantum Mechanics, Relativity, and Thermodynamics**  \n- 🤖 **Computational Mathematics with Python, NumPy, SymPy, and SciPy**  \n- 🔑 **Cryptography: RSA, Elliptic Curves, and Quantum Cryptography**  \n- 🎯 **Real-world Applications in Engineering, AI, and Cybersecurity**  \n\n---\n\n## 📂 Repository Structure  \n\n```\nMatrix-Singularity-and-Cipher/\n│── mathematics/        # Pure and Applied Mathematics\n│── physics/            # Classical and Quantum Physics\n│── computing/          # Computational Mathematics and Algorithms\n│── README.md           # Documentation\n```\n\n---\n\n## 🏁 Getting Started  \n\n### 1️⃣ Clone the Repository  \n```bash\ngit clone https://github.com/saadsalmanakram/Matrix-Singularity-and-Cipher.git\ncd Matrix-Singularity-and-Cipher\n```\n\n### 2️⃣ Install Dependencies  \n```bash\npip install -r requirements.txt\n```\n\n### 3️⃣ Run Example Scripts  \n```bash\npython mathematics/linear_algebra.py\npython physics/quantum_mechanics.py\npython cryptography/rsa_encryption.py\n```\n\n---\n\n## 🔍 Topics Covered  \n\n### 📖 **Mathematics**  \n- **Linear Algebra**: Vectors, Matrices, Eigenvalues, Singular Value Decomposition (SVD)  \n- **Calculus**: Differentiation, Integration, Partial Derivatives  \n- **Complex Numbers \u0026 Fourier Transforms**  \n- **Differential Equations \u0026 Chaos Theory**  \n- **Mathematical Optimization \u0026 Numerical Methods**  \n\n### 🔥 **Physics**  \n- **Classical Mechanics**: Newtonian Laws, Lagrangian \u0026 Hamiltonian Mechanics  \n- **Quantum Mechanics**: Schrödinger Equation, Quantum States, Superposition  \n- **Relativity**: Special \u0026 General Relativity, Time Dilation, Lorentz Transformation  \n- **Thermodynamics \u0026 Statistical Physics**  \n\n### 🤖 **Computational Mathematics**  \n- **Symbolic Mathematics with SymPy**  \n- **Numerical Computation with NumPy \u0026 SciPy**  \n- **Matrix Computations \u0026 Eigenvalue Problems**  \n- **Optimization \u0026 Scientific Computing**  \n\n### 🔑 **Cryptography \u0026 Secure Computing**  \n- **Classical Cryptography: Caesar Cipher, Vigenère Cipher**  \n- **Modern Cryptography: RSA, AES, Elliptic Curve Cryptography (ECC)**  \n- **Quantum Cryptography \u0026 Post-Quantum Cryptography**  \n\n---\n\n## 🔥 Example Code  \n\n### 🔨 **Solving a System of Linear Equations with NumPy**  \n```python\nimport numpy as np\n\nA = np.array([[2, -1], [4, 3]])\nb = np.array([3, 7])\n\nx = np.linalg.solve(A, b)\nprint(\"Solution:\", x)\n```\n\n### 🔥 **Quantum Mechanics: Solving Schrödinger’s Equation**  \n```python\nimport numpy as np\nimport scipy.linalg\n\n# Define a simple Hamiltonian matrix\nH = np.array([[0, 1], [1, 0]])\n\n# Compute eigenvalues and eigenvectors\neigenvalues, eigenvectors = scipy.linalg.eig(H)\nprint(\"Energy Levels:\", eigenvalues)\n```\n\n### 🔑 **RSA Encryption Implementation**  \n```python\nfrom Crypto.PublicKey import RSA\n\nkey = RSA.generate(2048)\nprivate_key = key.export_key()\npublic_key = key.publickey().export_key()\n\nprint(\"Public Key:\", public_key.decode())\nprint(\"Private Key:\", private_key.decode())\n```\n\n---\n\n## 🏆 Real-World Applications  \n\n✅ **Quantum Computing \u0026 Quantum Cryptography**  \n✅ **Secure Communication \u0026 Cybersecurity**  \n✅ **Machine Learning \u0026 AI Applications**  \n✅ **Physics Simulations \u0026 Chaos Theory**  \n✅ **Mathematical Modeling for Science \u0026 Engineering**  \n\n---\n\n## 🤝 Contributing  \n\nContributions are welcome! 🚀  \n\n🔹 **Fork** the repository  \n🔹 Create a new branch (`git checkout -b feature-name`)  \n🔹 Commit changes (`git commit -m \"Added Fourier Transform explanation\"`)  \n🔹 Push to your branch (`git push origin feature-name`)  \n🔹 Open a pull request  \n\n---\n\n## 📜 License  \n\nThis project is licensed under the **MIT License** – feel free to use, modify, and share the code.  \n\n---\n\n## 📬 Contact  \n\n📧 **Email:** saadsalmanakram1@gmail.com  \n🌐 **GitHub:** [SaadSalmanAkram](https://github.com/saadsalmanakram)  \n💼 **LinkedIn:** [Saad Salman Akram](https://www.linkedin.com/in/saadsalmanakram/)  \n\n---\n\n⚡ **Master Mathematics, Physics, and Computing Today!** ⚡  \n\n---\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsaadsalmanakram%2Fmatrix-singularity-and-cipher","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fsaadsalmanakram%2Fmatrix-singularity-and-cipher","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsaadsalmanakram%2Fmatrix-singularity-and-cipher/lists"}