willy-chan / qr-decomposition

Python program that uses numpy to perform the QR decomposition. This allows a user to decompose any real square input matrix into an orthogonal matrix (Q) multiplied by an upper triangular matrix (R).

Python QR Decomposition Calculator

This project utilizes the NumPy library to decompose any real square matrix into an orthogonal matrix (Q) multiplied by an upper triangular matrix (R).

Demo

Overview

The QR-Decomposition breaks down a matrix A into the product of two matrices: an orthogonal matrix Q and an upper triangular matrix R. The decomposition is represented mathematically as:

$A = QR$

where

• $A$ is the original input matrix
• $Q$ is the orthogonal matrix
• $R$ is the upper triangular matrix

The orthogonal matrix $Q$ has the property $Q^T * Q = I$, where $Q^T$ denotes the transpose of $Q$ and $I$ is the identity matrix. The upper triangular matrix $R$ contains the transformed values of the original matrix $A$.

Usage

To use the QR-Decomposition project, follow these steps:

• Ensure that you have NumPy installed. You can install it using the following command:

pip install numpy

• Open the Python script in your preferred code editor.
• Provide the matrix A that you want to decompose. You can specify the matrix by modifying the input array in the code.
• Run the script. The program will perform the QR-Decomposition and output the resulting orthogonal matrix $Q$ and upper triangular matrix $R$.

Please note that the QR-Decomposition project utilizes NumPy's built-in functions to perform the decomposition. It is designed for real square matrices.

Support

If you encounter any issues or have questions regarding the QR-Decomposition project, please feel free to open an issue on the GitHub repository or contact me personally at [email protected]

License

The QR-Decomposition project is released under the MIT License. You are free to use, modify, and distribute the code in accordance with the terms and conditions of the license.