random matrix A:
     -1.19      -1.54     -0.943      -1.16 
     -1.71     -0.853      -1.62     -0.415 
    -0.936      -1.98      -1.84     -0.653 
     -1.57      -1.63      -1.46      -1.57 
random vector b:
     0.531      0.861      0.839      0.507 
givnesQR: solution x to system A*x=b:
    -0.451      -0.41     0.0265      0.528 
GSQR    : solution x to system A*x=b:
    -0.451      -0.41     0.0265      0.528 
check: A*x (should be equal b):
     0.531      0.861      0.839      0.507 
test passed
givens:
A^-1*A=
         1   2.22e-16          0  -4.44e-16 
 -4.44e-16          1   8.88e-16   4.44e-16 
  4.44e-16  -1.33e-15          1  -8.88e-16 
  4.44e-16  -4.44e-16  -4.44e-16          1 
givens:
A*A^-1=
         1  -3.33e-16   3.89e-16  -4.44e-16 
 -1.78e-15          1   3.19e-16   1.11e-16 
 -7.77e-16          0          1   4.44e-16 
 -4.44e-16   2.22e-16          0          1 
GramSchmidt:
A^-1*A=
         1  -2.09e-14  -2.04e-14  -1.42e-14 
 -2.04e-14          1  -2.04e-14  -1.42e-14 
  2.66e-14   2.66e-14          1   1.87e-14 
     2e-14   2.04e-14      2e-14          1 
GramSchmidt:
A*A^-1=
         1  -1.89e-15  -2.22e-16  -8.88e-16 
 -2.22e-15          1   1.01e-15   1.11e-15 
 -1.22e-15   3.89e-16          1   4.44e-16 
 -8.88e-16   6.66e-16   1.17e-15          1 

tall matrix:
random matrix A:
     -1.45      -1.46     -0.837 
     -1.76      -1.35      -1.14 
      -0.7      -1.76     -0.574 
     -1.09      -1.13      -1.81 

pinvA (pseudo inverse of A):
    -0.442     -0.754       0.64      0.475 
   -0.0361      0.307     -0.831     0.0874 
     0.328       0.23      0.122     -0.886 

pinvA*A:
         1   2.22e-15   1.78e-15 
 -1.29e-15          1  -9.99e-16 
 -1.33e-15  -1.33e-15          1