This tool is designed for mathematicians, engineers, and students who need to perform QR decomposition on matrices. It simplifies the process, making it accessible and efficient.
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Data Source and Methodology
All calculations are based on linear algebra principles. For more details, refer to eMathHelp. All calculations are based on reliable mathematical formulas.
The Formula Explained
The QR decomposition of a matrix \( A \) is given by \( A = QR \), where \( Q \) is an orthogonal matrix and \( R \) is an upper triangular matrix.
Glossary of Terms
- Matrix A: The input matrix to be decomposed.
- Matrix Q: An orthogonal matrix resulting from the decomposition.
- Matrix R: An upper triangular matrix resulting from the decomposition.
How It Works: A Step-by-Step Example
For matrix \([1,2;3,4]\), the QR decomposition results in matrices Q and R such that their product reconstructs the original matrix.
Frequently Asked Questions (FAQ)
What is QR Decomposition?
QR decomposition is a method used in linear algebra to decompose a matrix into a product of an orthogonal matrix and an upper triangular matrix.
Why use QR Decomposition?
It is often used to solve linear systems and for eigenvalue problems.