# QR decomposition

(1 hours to learn)

## Summary

The operations of the Gram-Schmidt procedure can be represented as a factorization of a matrix into an orthogonal matrix Q and an upper triangular matrix R. This is a useful representation for solving linear least squares problems.

## Context

This concept has the prerequisites:

- orthonormal bases (The Gram-Schmidt procedure is a simple algorithm for computing the QR decomposition.)

## Core resources (read/watch one of the following)

## -Free-

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 4.4, "Orthogonal bases and Gram-Schmidt," subsection "The factorization A = QR," pages 235-238

## See also

- The Gram-Schmidt procedure is not numerically stable. In practice, we would compute the QR decomposition using one of: