The QRDecomposition command computes the QR decomposition of the Matrix A, that is, a factorization into a product of an orthogonal (or unitary) Matrix, Q, and an upper triangular Matrix, R, such that $A=Q·R$.  The Matrices Q and R are returned in an expression sequence.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$A≔⟨⟨1\,2\,3⟩|⟨4\,5\,6⟩⟩$

$A≔\left[\begin{array}{cc}1& 4\\ 2& 5\\ 3& 6\end{array}\right]$

$Q,R≔\mathrm{QRDecomposition}\left(A\right)$

$Q,R≔\left[\begin{array}{ccc}\frac{\sqrt{14}}{14}& \frac{4\sqrt{21}}{21}& \frac{\sqrt{6}}{6}\\ \frac{\sqrt{14}}{7}& \frac{\sqrt{21}}{21}& -\frac{\sqrt{6}}{3}\\ \frac{3\sqrt{14}}{14}& -\frac{2\sqrt{21}}{21}& \frac{\sqrt{6}}{6}\end{array}\right],\left[\begin{array}{cc}\sqrt{14}& \frac{16\sqrt{14}}{7}\\ 0& \frac{3\sqrt{21}}{7}\\ 0& 0\end{array}\right]$

$\mathrm{Equal}\left(Q·R\,A\right)$

$\mathrm{true}$