Definition:QR Factorization

Definition

Let $\mathbf A$ be a matrix of order $m \times n$ such that $m \ge n$.

A QR factorization of $\mathbf A$ is a factorization of $\mathbf A$:

$\mathbf A = \mathbf Q \mathbf R$

where:

$\mathbf Q$ consists of column vectors which are orthonormal

$\mathbf R$ is an upper triangular matrix.

Also see

• Gram-Schmidt Orthogonalization

• Results about QR factorizations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): QR factorization
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): QR factorization