Linear Algebra Matrix Database

A web-based tool for exploring and searching matrices based on their mathematical properties. This project helps users find matrix examples that satisfy specific properties while respecting mathematical rules and theorems.

Features

🔍 Matrix Search

• Search for matrices by including or excluding specific properties
• Smart property suggestions with auto-complete
• Support for multiple comma-separated properties
• Case-insensitive search

📦 Matrix Database

• Organized collection of matrices with their properties
• Each matrix entry includes:
  • Name/identifier
  • List of properties (tags)
  • Unique ID for reference

📜 Logical Rules Engine

The system enforces mathematical theorems and properties through logical rules. For example:

• Spectral Theorem: Real symmetric matrices are diagonalizable with real eigenvalues
• Complex Spectral Theorem: Hermitian matrices are diagonalizable with real eigenvalues
• Property exclusions: Matrices with real eigenvalues cannot have pure imaginary eigenvalues

🛠️ Administration

• Interface for proposing changes to the database
• Structured data format for matrices and rules

Usage

1. Search for Matrices

   • Use the "Proprietà incluse" field to specify required properties
   • Type partial property names for suggestions
   • Add multiple properties using commas
   • Use arrow keys or mouse to select from suggestions

2. Exclude Properties

   • Use the "Proprietà escluse" field to specify properties you don't want
   • Works with the same suggestion system as inclusion

3. View Results

   • Click "Cerca" to search
   • Results show matching matrices and their properties
   • System checks for rule violations before showing results

4. Propose Changes

   • Click "🛠️ Proponi una modifica al database" to suggest additions or modifications

Data Structure

Matrix Entry Format (data/database.json):

{
  "id": 1,
  "nome": "Matrix Name",
  "tags": ["property1", "property2", ...]
}

Rule Format (data/regole.json):

{
  "id": 1,
  "nome": "Rule Name",
  "se": [
    {"tag": "property1", "negato": false},
    {"tag": "property2", "negato": true}
  ],
  "allora": [
    {"tag": "result1", "negato": false}
  ]
}

Local Development

1. Clone the repository
2. Serve the directory using a local HTTP server:

   python3 -m http.server 8000

3. Visit http://localhost:8000 in your browser

Contributing

To contribute new matrices or rules:

1. Use the admin interface to propose changes
2. Ensure new entries follow the existing JSON structure
3. Verify that new rules are mathematically sound

License

This project is part of educational resources for Linear Algebra. Please check with the repository owner for specific licensing terms.