NumPy Complex Linear Algebra Workshops

Educational project implementing complex linear algebra operations through interactive Jupyter notebooks that solve specific workshop assignments.

Overview

This project provides complete solutions to 4 workshops focusing on complex linear algebra using NumPy. Each notebook implements the exact requirements specified in the tasks/ folder, progressing from basic complex number operations to advanced quantum computing applications.

Workshop Solutions

Workshop 1: Complex Number Fundamentals

File: Taller1_ComplexIntro.ipynb
Tasks: tasks/Taller Espacios Vectoriales Complejos.pdf

Complete introduction to complex numbers including:

• Cartesian and polar representation
• Basic operations and complex arithmetic
• Modulus and phase calculations
• Complex conjugates and properties

Workshop 2: Vector and Matrix Operations

File: Taller2_Vector_Matrix_Operations.ipynb
Tasks: tasks/Taller Espacios Vectoriales Complejos 2.pdf

Advanced vector and matrix manipulations:

• Complex column vector creation and operations
• Matrix addition, scalar multiplication
• Matrix-vector products and transformations
• Complex matrix conjugates and transposes

Workshop 3: Vector Spaces and Eigenvalues

File: Taller3_Inner_Products_Eigenvalues.ipynb
Tasks: tasks/Taller Espacios Vectoriales Complejos 3.pdf

Inner product spaces and spectral analysis:

• Complex inner products and norms
• Eigenvalue and eigenvector computation
• Distance and angle calculations in complex spaces
• Orthogonality and normalization

Workshop 4: Advanced Matrix Theory

File: Taller4_Hermitian_Unitary_Tensor.ipynb
Tasks: tasks/Taller Espacios Vectoriales Complejos 4.pdf

Specialized matrices and quantum applications:

• Hermitian matrix analysis and properties
• Unitary matrices and transformations
• Tensor products and composite systems
• Quantum state evolution and measurements

Project Structure

numpy-complex-py/
├── Taller1_ComplexIntro.ipynb           # Workshop 1 solution
├── Taller2_Vector_Matrix_Operations.ipynb  # Workshop 2 solution
├── Taller3_Inner_Products_Eigenvalues.ipynb # Workshop 3 solution  
├── Taller4_Hermitian_Unitary_Tensor.ipynb  # Workshop 4 solution
├── tasks/                               # Original workshop assignments
│   ├── Taller Espacios Vectoriales Complejos.pdf
│   ├── Taller Espacios Vectoriales Complejos 2.pdf
│   ├── Taller Espacios Vectoriales Complejos 3.pdf
│   └── Taller Espacios Vectoriales Complejos 4.pdf
├── requirements.txt                     # Python dependencies
├── README.md                           # This file
└── LICENSE                            # GPL-3.0 License

Installation and Usage

1. Clone the repository:

   git clone https://github.com/AnderssonProgramming/numpy-complex-py.git
   cd numpy-complex-py

2. Install dependencies:

   pip install -r requirements.txt

3. Launch Jupyter and open any workshop notebook:

   jupyter notebook

Requirements

• Python 3.8+
• NumPy 1.21+
• Jupyter Notebook
• Matplotlib (for visualizations)

Contributing

1. Fork the repository
2. Create your feature branch (git checkout -b feature/AmazingFeature)
3. Commit your changes (git commit -m 'feat: add some amazing feature')
4. Push to the branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

Please use conventional commit messages (feat, fix, docs, test, chore, etc.).

Versioning

We use SemVer for versioning. For the versions available, see the tags on this repository.

Authors

• Andersson Programming - Initial work - AnderssonProgramming

License

GPL-3.0 License - see LICENSE file for details.

Acknowledgments

Complex Number Operations

• Complex arithmetic and properties
• Cartesian ↔ Polar conversions
• Modulus and argument calculations

Vector Spaces

• Complex vector operations
• Inner products and norms
• Orthogonality and projections

Matrix Theory

• Complex matrix operations
• Eigenvalue decomposition
• Hermitian and unitary matrices
• Tensor products

Quantum Applications

• State vector representation
• Unitary evolution
• Measurement operators
• Composite quantum systems