random matrix A:
     -1.27      -1.72    -0.0561     -0.226 
    -0.987      -1.34      -1.73     -0.383 
    -0.589     -0.396       -1.8      -1.12 
   -0.0643      -1.82     -0.646     -0.393 
random vector b:
    0.0102      0.341     0.0603      0.322 
GivnesQR: solution x to system A*x=b:
     0.171     -0.162     -0.233      0.288 
GSQR    : solution x to system A*x=b:
     0.171     -0.162     -0.233      0.288 
check: A*x (should be equal b):
    0.0102      0.341     0.0603      0.322 
test passed
Givens:
A^-1*A=
         1  -2.22e-16  -2.78e-16  -1.11e-16 
  2.08e-17          1   5.55e-17   5.55e-17 
  3.63e-16   1.18e-16          1  -3.47e-18 
 -4.96e-16  -2.22e-16  -9.99e-16          1 
Givens:
A*A^-1=
         1  -3.89e-16   5.55e-17  -4.16e-17 
  5.55e-17          1  -1.11e-16  -3.47e-16 
         0  -2.22e-16          1  -1.11e-16 
  5.55e-17          0          0          1 
GramSchmidt:
A^-1*A=
         1  -2.22e-16   2.22e-16   1.67e-16 
 -3.26e-16          1  -3.33e-16  -1.39e-16 
 -2.26e-17  -4.16e-17          1   1.39e-17 
  2.08e-17  -5.55e-16  -9.16e-16          1 
GramSchmidt:
A*A^-1=
         1  -1.67e-16   5.55e-17  -3.75e-16 
  1.11e-16          1          0  -2.22e-16 
 -1.11e-16   2.22e-16          1  -3.89e-16 
  -2.5e-16  -2.22e-16  -2.78e-16          1 

tall matrix:
random matrix A:
    -0.589     -0.227      -1.65 
    -0.921      -1.23     -0.168 
    -0.355     -0.833     -0.968 
     -1.73     -0.154      -1.04 

pinvA (pseudo inverse of A):
     0.235     -0.172      0.305     -0.628 
    0.0723     -0.587     -0.423      0.374 
    -0.531      0.273     -0.276     0.0917 

pinvA*A:
         1   1.53e-16          0 
 -3.33e-16          1  -2.22e-16 
 -1.11e-16  -1.27e-16          1