QR decomposition

In linear algebra, the QR decomposition of a matrix A is a factorization expressing A as

A = QR

where Q is an orthogonal matrix (QQ^T = I), and R is an upper triangular matrix.

The QR decomposition is often used to solve the linear least squares problem. The QR decomposition is also the basis for a particular eigenvalue algorithm, the QR algorithm.

Actual methods to calculate the QR decomposition include Givens rotations, Householder transformations and the Gram-Schmidt decomposition.