qr
Q-R decomposition of a matrix.
(Q, R, E)=qr(a)
(Q, R)=qr(a)
Inputs
a Any matrix.
Outputs
Q A unitary matrix (satisfying Q'Q=I , where I is the identity matrix.
R An upper triangualr matrix.
E A matrix in which each column or each row has a single nonzero entry, which is one.


Description
The outputs satisfy Q*R=a or, when three outputs are used, Q*R=a*E' . In the latter case column exchanges are used to compute the Q-R decomposition, and the information on the exchanges is output in the matrix E .
Example
>>a=[1 2 3 4;5 6 7 8; 9 0 11 12];
>>(q,r)=qr(a)
>>q
   -0.0967   -0.3083    0.9463
   -0.4834   -0.8166   -0.3154
   -0.8701    0.4879    0.0701

>>r
  -10.3441   -3.0936  -13.2443  -14.6944
         0   -5.5163   -1.2740   -1.9111
         0         0    1.4020    2.1030

>>q'*q
    1.0000         0         0
         0    1.0000         0
         0         0    1.0000

>>norm(q*r-a)
      6.2172e-015