##  [QR Decomposition](/index.php/qr-decomposition) 

  ##  [QR Decomposition](https://natural.quantumdictionary.io/qr-decomposition-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/index.php/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A matrix factorization A = Q R where Q is orthogonal (or unitary) and R is upper triangular; variants include full and reduced (thin) forms. It is used for solving linear systems, least-squares problems, and as a building block in numerical eigenvalue algorithms.