Numerical-Linear-Algebra
Learn Linear Algebra via Programming
This repository is aimed at providing an introduction to the basics of linear algebra and advanced computational numerical linear algebra with a focus on applications in quantum computing.
Quantum computing is a rapidly growing field that has the potential to revolutionize the way we process and analyze information. Linear algebra forms an essential part of the mathematical framework used in quantum computing. In this article, we will explore the role of linear algebra in quantum computing, including its importance in representing quantum states, quantum gates, and quantum algorithms.
Check the full Blog series here
Table
Content
Introduction to Linear Algebra
This section of the repository will cover the basics of linear algebra. It will include topics such as vectors, matrices, linear transformations, and eigenvalues/eigenvectors. The content will be presented in a way that is accessible to beginners, with examples and exercises to solidify understanding.
| Serial Number | Title | Description | Links | Medium |
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| 1 | Scalars, vectors, matrices and tensors | Introduction to basic concepts in linear algebra |  |
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| 2 | Multiplying matrices and vectors | Understanding how matrix multiplication works | |
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| 3 | Identity and inverse matrices | Explanation of identity and inverse matrices | |
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| 4 | Linear dependence and span | Understanding linear dependence and span of vectors | |
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| 5 | Norms | Definition and examples of vector norms | |
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| 6 | Special kind of matrices | Introduction to special types of matrices | |
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| 7 | Eigendecomposition | Understanding eigenvectors and eigenvalues | |
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| 8 | Singular value decomposition | Introduction to singular value decomposition | |
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| 9 | The Moore-Penrose pseudoinverse | Definition and applications of the pseudoinverse | |
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| 10 | The trace operator | Definition and properties of the trace operator | |
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| 11 | The determinant | Explanation of the determinant of a matrix | |
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Use cases of Linear Algebra
This section of the repository will cover advanced topics in computational numerical linear algebra. It will include topics such as singular value decomposition (SVD), QR decomposition, and LU decomposition. The content will be presented with a focus on their applications in quantum computing, and will include exercises and projects to solidify understanding.
| Serial Number | Title | Description | Links | Medium |
|---|---|---|---|---|
| 1 | Introduction to matrices | Overview of matrices and their properties, operations, and applications | |
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| 2 | Singular Value Decomposition | Introduction to singular value decomposition and its applications | |
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| 3 | Topic Modelling with NMF | Explanation of Non-negative Matrix Factorization for topic modeling | |
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| 4 | Background Removal | Techniques for removing the background from images using linear algebra | |
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| 5 | Compressed Sensing CT scans | Using compressed sensing for faster and more efficient CT scans | |
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| 6 | Health outcomes with linear algebra | Applications of linear algebra in healthcare and medical research | |
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| 7 | Linear regression | Introduction to linear regression and its applications | |
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| 8 | Page rank with eigen decomposition | Explanation of PageRank algorithm using eigendecomposition | |
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Applications in Quantum Computing
| Serial Number | Title | Description | Links | Medium |
|---|---|---|---|---|
| 1 | Introduction to Complex Arithemetic | This is a tutorial designed to introduce you to complex arithmetic. | |
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| 2 | Introduction to Linear Algebra | This is a tutorial designed to introduce you to Linear Algebra. | |
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| 3 | Single Qubit Gates | This is a tutorial designed to introduce you to Linear Algebra. in single qubit gates | |
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| 4 | Multiple Qubits | This is a tutorial designed to introduce you to Linear Algebra in multiple qubit operations. | |
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This section of the repository will cover the applications of linear algebra and computational numerical linear algebra in quantum computing. It will include topics such as quantum gates, quantum circuits, and quantum algorithms. The content will be presented in a way that is accessible to beginners, with examples and exercises to solidify understanding. This will be covered in detail in another repository.
Getting Started
These instructions will get you a copy of the project up and running on your local machine for development and testing purposes.
Prerequisites
This project requires Python 3.x and Jupyter Notebook. You can install Python from the official Python website and Jupyter Notebook can be installed using the following command:
pip install jupyter
Installation
To get started, simply clone the repository:
git clone https://github.com/MonitSharma/Numerical-Linear-Algebra.git
Usage
You will find the content organized into directories according to the topics covered in this repository. The examples and exercises are provided in Jupyter notebooks that can be run on your local machine. To run the Jupyter notebooks, navigate to the directory containing the notebooks and type the following command in the terminal:
jupyter notebook
This will start the Jupyter Notebook server and open a web page in your browser. Click on the notebook you want to open and start exploring the content.
Contributing
Contributions are welcome! Please feel free to open an issue if you find a bug or have a suggestion for improvement. Pull requests are also welcome.
License
This repository is licensed under the MIT License.
Acknowledgements
We would like to thank the following resources for their contribution to this repository:
- Linear Algebra - Khan Academy
- Numerical Linear Algebra for Coders - Fast.ai
- Quantum Computing for the Very Curious - IBM