RQ decomposition from QR decomposition

[daviddoria]

What I'm wondering is:

Q and R in the QR decomposition of A are the same Q and R in the RQ decomposition of which matrix?

I found some MATLAB code which will get RQ from QR, but I don't understand how you would do those operations FIRST, then find the QR decomposition.

ReverseRows = [0 0 1; 0 1 0 ; 1 0 0];
[Q R] = qr((ReverseRows * A)');
R = ReverseRows * R' * ReverseRows;
Q = ReverseRows * Q';

Any tips about the intuition of the relations of these factorizations?

Thanks,
Dave

 

[daviddoria]

I guess what I was looking for is that QR is Gram-Schmidt applied to the column of A, where RQ is Gram-Schmidt applied to the rows of A.

Dave