QRDecomposition - Maple Help
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Student[LinearAlgebra]

 QRDecomposition
 compute the QR factorization of a Matrix

 Calling Sequence QRDecomposition(A, options)

Parameters

 A - Matrix options - (optional) parameters; for a complete list, see LinearAlgebra[QRDecomposition]

Description

 • 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.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{LinearAlgebra}}\right):$
 > $A≔⟨⟨1,2,3⟩|⟨4,5,6⟩⟩$
 ${A}{≔}\left[\begin{array}{cc}{1}& {4}\\ {2}& {5}\\ {3}& {6}\end{array}\right]$ (1)
 > $Q,R≔\mathrm{QRDecomposition}\left(A\right)$
 ${Q}{,}{R}{≔}\left[\begin{array}{ccc}\frac{\sqrt{{14}}}{{14}}& \frac{{4}{}\sqrt{{21}}}{{21}}& \frac{\sqrt{{6}}}{{6}}\\ \frac{\sqrt{{14}}}{{7}}& \frac{\sqrt{{21}}}{{21}}& {-}\frac{\sqrt{{6}}}{{3}}\\ \frac{{3}{}\sqrt{{14}}}{{14}}& {-}\frac{{2}{}\sqrt{{21}}}{{21}}& \frac{\sqrt{{6}}}{{6}}\end{array}\right]{,}\left[\begin{array}{cc}\sqrt{{14}}& \frac{{16}{}\sqrt{{14}}}{{7}}\\ {0}& \frac{{3}{}\sqrt{{21}}}{{7}}\\ {0}& {0}\end{array}\right]$ (2)
 > $\mathrm{Equal}\left(\mathrm{.}\left(Q,R\right),A\right)$
 ${\mathrm{true}}$ (3)