matrixlab 0.0.1
A numerical linear algebra library in native Python
License: MIT License

# matrixlab: A Library for Numerical Linear Algebra and Linear System Solvers

**matrixlab** is a Python library designed to provide a broad suite of fundamental numerical linear algebra methods and algorithms. Built for researchers, educators, and practitioners, it offers a versatile and reliable resource for solving mathematical problems across various domains, including data science, machine learning, and scientific computing.

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## Why matrixlab?

matrixlab, short for **"Numerical Matrix and Linear Algebra Toolkit"**, focuses on clarity, accuracy, and accessibility. It bridges the gap between theoretical linear algebra and practical applications, making complex concepts approachable and usable for diverse audiences. Whether solving large-scale computational problems, conducting academic research, or teaching numerical methods, matrixlab is designed to support your needs.

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## Key Features

- **Comprehensive Functionality**: matrixlab includes essential tools such as:
  - LU, QR, and Cholesky factorizations.
  - Iterative solvers like Conjugate Gradient (CG) and GMRES.
  - Eigenvalue decompositions.
  - Preconditioning techniques for linear systems.
  - Rank-revealing factorizations.
  
- **Sparse Matrix Support**: All operations are performed on sparse matrices in CSR (Compressed Sparse Row) format for efficiency and scalability.

- **User-Friendly Design**: matrixlab provides an intuitive Python API with clear and consistent interfaces, ensuring ease of use for both beginners and advanced users.

- **Versatile Applications**: matrixlab supports a wide range of applications, including:
  - Solving systems of linear equations.
  - Dimensionality reduction techniques for data science.
  - Stability analysis in engineering systems.
  - Optimization and inverse problems in scientific research.

- **Educational Utility**: The library is an excellent resource for teaching and learning numerical methods. It includes detailed documentation, illustrative examples, and explanatory notes to deepen understanding.

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## Module Overview

| Module | Description |
|--------|------------|
| [`lssolvers`](matrixlab/lssolvers) | Solvers for least square problems |
| [`lrank`](matrixlab/lrank) | Low-rank approximation methods |
| [`preconditioners`](matrixlab/preconditioners) | Preconditioners for linear systems |
| [`esolvers`](matrixlab/esolvers) | Eigenvalue solvers |
| [`gallery`](matrixlab/gallery) | Test matrices for numerical experiments |

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## Getting Started

### Installation

matrixlab is available on PyPI. To install, simply run:

```bash
pip install matrixlab
```


### Documentation and Examples

Detailed documentation and additional examples are available on the [matrixlab website](https://matrixlab.org) and in the repository’s `/examples` folder.

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## Applications

matrixlab is designed for a broad range of use cases, including:

- **Scientific Computing**: Perform matrix computations efficiently and accurately for simulations and modeling.
- **Data Science and Machine Learning**: Use matrix decompositions and iterative solvers for preprocessing and analyzing large datasets.
- **Engineering and Physics**: Solve systems of equations, perform eigenvalue analysis, and optimize complex models.
- **Educational Purposes**: Teach and learn numerical linear algebra concepts through hands-on coding and well-documented examples.

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## Contributing

matrixlab is an open-source project, and contributions are welcome! Whether fixing bugs, adding new features, or improving documentation, your help is appreciated.


## License

matrixlab is licensed under the MIT License. See the `LICENSE` file for details.

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## Join the Community

Stay updated and connect with the matrixlab community:

- [GitHub Repository](https://github.com/open-sciml/matrixlab)

Discover, solve, and learn with **matrixlab** — your comprehensive Python library for numerical linear algebra!