qz
QZ decomposition of a pair of real matrices.
(at, bt, Q, Z)=qz(a, b)
Inputs
a A real square matrix.
b A real square matrix of the same size as a .
Outputs
at A matrix of the same size as the inputs with zeros below the main sub-diagonal to the left of the main diagonal.
bt A matrix of the same size as the inputs with zeros below the main sub-diagonal to the left of the main diagonal.
Q A unitary matrix of the same size as the inputs.
Z A unitary matrix of the same size as the inputs.


Description
The matrices at and bt are related to the inputs via the transformations at=Q'*a*Z and bt=Q'*b*Z .
Example
>>a=[1 2 3;5 7 9; 13 12 15]
>>b=[12 19 23; 76 89 19; 12 16 31]
>>a
          1          2          3
          5          7          9
         13         12         15

>>b
         12         19         23
         76         89         19
         12         16         31

>>[at,bt,Q,Z]=qz(a,b)
>>at
      -4.0413      22.6403      -8.0551
            0       10.464      -1.9034
            0            0       0.2838

>>bt
      -3.1528      44.5148     -12.0142
            0      78.1416     -85.2491
            0            0      30.7185

>>at-Q'*a*Z
Scaled by 10^-13
       0.0888      -0.9948       0.2842
      -0.0422       0.7638      -0.1665
      -0.1024       1.5123      -0.3331

>>bt-Q'*b*Z
Scaled by 10^-12
         0.02      -0.6466       0.5365
       0.0173       0.3411      -0.2984
      -0.0058       0.8082      -0.6608