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QRDecomposition
QRDecomposition[
m
] yields the QR decomposition for a numerical matrix m. The result is a list 
q
,
r
 , where q is an orthogonal matrix and r is an upper triangular matrix.
The original matrix m is equal to Conjugate[Transpose[
q
]]
.
r.
For non-square matrices, q is row orthonormal.
The matrix r has zeros for all entries below the leading diagonal.
QRDecomposition[
m
,
Pivoting
->
True] yields a list 
q
,
r
,
p
 where p is a permutation matrix such that m
.
p is equal to Conjugate[Transpose[
q
]]
.
r.
See the Mathematica book: Section 3.7.10.
See also Implementation NotesA.9.44.27MainBookLinkOldButtonDataA.9.44.27.
See also: SchurDecomposition, LUDecomposition, SingularValues, JordanDecomposition.
Related package: LinearAlgebra`Cholesky`, LinearAlgebra`Orthogonalization`.
Further Examples
Performing a QRDecomposition on this  x  matrix yields a pair of matrices.
In[1]:= 
Out[1]= 
This checks the result.
In[2]:= 
Out[2]//MatrixForm= 
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