Matrix

Matrix is a web-based matrix calculator built with Flask. It provides a user-friendly interface to perform a wide range of matrix operations, from basic arithmetic to advanced applications like message encryption and decryption.

Features

• Basic Arithmetic: Addition, subtraction, and multiplication of matrices.
• Scalar Operations: Multiply a matrix by a scalar value.
• Advanced Calculations:
  • Matrix Transpose
  • Determinant (for square matrices of any size via Laplace expansion)
  • Matrix Inverse (using the adjugate method)
• Cryptography:
  • Encrypt text messages using an invertible encoding matrix (a form of Hill Cipher).
  • Decrypt messages using the inverse of the encoding matrix.
• Dynamic UI: The interface dynamically generates input fields based on user-specified matrix dimensions.
• Data Export: Export the results of operations (including the input matrices) to JSON, XML, or HTML formats.
• Error Handling: Validates matrix dimensions and mathematical conditions (e.g., non-singular matrices for inversion) and provides clear error messages.

Technology Stack

• Backend: Python, Flask
• Frontend: HTML, CSS, JavaScript (Vanilla)
• Math Engine: Custom Matrix class with core logic in Python.
• Testing: Pytest
• CI/CD: GitHub Actions

Installation and Usage

To get a local copy up and running, follow these steps.

1. Clone the repository:

   git clone https://github.com/tskxz/matrix.git
   cd matrix

2. Create and activate a virtual environment:

   • On macOS/Linux:

     python3 -m venv venv
     source venv/bin/activate

   • On Windows:

     python -m venv venv
     .\venv\Scripts\activate

3. Install dependencies:

   pip install -r requirements.txt

4. Run the application:

   python app.py

5. Open your browser and navigate to http://127.0.0.1:5000.

Running Tests

The project includes a suite of unit tests to ensure the correctness of the matrix operations. To run the tests:

python -m pytest tests/ -v -s

Project Structure

The repository is organized as follows:

├── app.py                  # Main Flask application with all routes
├── core/
│   └── matrix.py           # Core Matrix class with all mathematical logic
├── static/
│   ├── css/                # CSS stylesheets
│   └── js/                 # Frontend JavaScript for each operation
├── templates/              # HTML templates for the web interface
├── tests/
│   ├── test_matrix.py      # Unit tests for the Matrix class
│   └── test_routes.py      # Unit tests for the Flask routes
├── docs/                   # System analysis, diagrams, and documentation
├── requirements.txt        # Python dependencies
└── .github/                # CI workflows and PR templates

Cryptography Implementation

The application uses matrix multiplication for encryption and decryption, a method similar to the Hill Cipher.

1. Character Mapping: Each character in the message is converted to a number based on a predefined map (A=1, B=2, ..., ' '=29).
2. Message Matrix: The resulting sequence of numbers is organized into a matrix (M). The number of rows of this matrix matches the dimensions of the encoding matrix.
3. Encryption: The message matrix M is multiplied by a user-provided, invertible encoding matrix A to produce the encrypted matrix N.
   • N = A * M
4. Decryption: To recover the original message, the encrypted matrix N is multiplied by the inverse of the encoding matrix, A⁻¹.
   • M = A⁻¹ * N
5. Conversion to Text: The numbers in the resulting matrix M are converted back to characters to reveal the original message.

An encoding matrix must be invertible (i.e., its determinant must be non-zero) for decryption to be possible. The application validates this condition before performing any encryption.

License

This project is licensed under the MIT License. See the LICENSE file for details.