QR and permutation matrix
10-26-2015, 03:04 PM (This post was last modified: 10-26-2015 03:18 PM by Han.)
Post: #1
 Han Senior Member Posts: 1,882 Joined: Dec 2013
QR and permutation matrix
The QR() command returns the QR factorization of a matrix and includes a permutation matrix. I cannot seem to find an example of a matrix for which the QR factorization returns a permutation matrix that is non-identity. Is anyone able to find such a case? From the looks of it, the QR() command does not appear to do any pivoting (the diagonals of R are not in non-increasing order). For example:

M2:=[[1,2],[3,5],[-1,7],[2,-1]]
QR(M2);

returns

Code:
[   [0.258198889747,0.169657961696,0.94436252598,−0.112822554889],   [0.774596669241,0.393298002112,−0.326894720531,−0.372097464682],   [−0.258198889747,0.871424985073,−3.63216356146e−2,0.415490755024],   [0.516397779494,−0.23906349148,0,0.82230285198] ], [   [3.87298334621,2.06559111798],   [0,8.64484432094],   [0,0],   [0,0] ], [   [1,0,0,0],   [0,1,0,0],   [0,0,1,0],   [0,0,0,1] ]

So is there no pivoting? And if not, then it appears the P matrix is superfluous.

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 Messages In This Thread QR and permutation matrix - Han - 10-26-2015 03:04 PM RE: QR and permutation matrix - parisse - 10-26-2015, 05:04 PM RE: QR and permutation matrix - Han - 10-26-2015, 07:24 PM RE: QR and permutation matrix - Han - 10-26-2015, 05:16 PM RE: QR and permutation matrix - parisse - 10-27-2015, 06:48 AM

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