The QRDecomposition(M) calling sequence displays a Maplet application that returns the QR decomposition of the matrix M.

A definition of the QR decomposition of a matrix is given in the Maplet application.

By selecting the Full QR factorization check box, force the routine to perform the full QR factorization, which is generally performed only if M has full rank.

By using the Output drop-down box, control the output returned to the worksheet.

Note: If M has floating-point entries and R and rank are included in the Output, the rank returned is not the rank of M. For more information, see LinearAlgebra[QRDecomposition].

By using the Matrix has real values check box, control the algorithm used. If the matrix has real entries, a faster algorithm can be used. The default value is determined by using the value of $\mathrm{has}\left(M\,\mathrm{I}\right)$, which returns true if M has complex entries. That is, it is selected, by default, only if M has no complex entries.

Note: If Matrix has real values is selected and the matrix has any complex entries, an incorrect result may be returned.

By using the Upper-triangular shape and storage for R check box, control the form of the matrix R returned.

By using the Return read-only matrix(ces) check box, control whether the matrix(ces) returned by the Maplet application are read-only. The default behavior is that the matrix(ces) returned are not read-only.

By using the Evaluate result check box, control whether the Maplet application returns the output requested or the calling sequence required to calculate this output in the worksheet. The default behavior is to evaluate the result, that is, return the requested output.

The QRDecomposition sample Maplet worksheet demonstrates how to write a Maplet application that functions similarly to the Maplet application displayed by this routine.

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

$\mathrm{QRDecomposition}\left(⟨⟨1\,3⟩\left|⟨2\,5⟩\right|⟨5\,7⟩⟩\right)$