QR decomposition:
some random matrix A:
   0.840    0.394    0.783 
   0.798    0.912    0.198 
   0.335    0.768    0.278 
   0.554    0.477    0.629 
matrix Q:
   0.633   -0.578    0.156 
   0.601    0.314   -0.712 
   0.252    0.752    0.439 
   0.417   -0.031    0.525 
matrix R:
   1.328    1.191    0.947 
   0.000    0.621   -0.201 
   0.000    0.000    0.433 
matrix Q^TQ (should be 1):
   1.000   -0.000   -0.000 
  -0.000    1.000    0.000 
  -0.000    0.000    1.000 
matrix QR (should be equal A):
   0.840    0.394    0.783 
   0.798    0.912    0.198 
   0.335    0.768    0.278 
   0.554    0.477    0.629 

Linear System: 
main: a random square matrix A:
   0.365    0.513    0.952 
   0.916    0.636    0.717 
   0.142    0.607    0.016 
main: a random right-hand side b : 0.242887 0.137232 0.804177 
main: solution x : Ax=b          : -0.647301 1.48389 -0.297009 
main: Ax, should be equal b      : 0.242887 0.137232 0.804177 
main: inverse matrix A^{-1}:
  -1.275    1.709   -0.711 
   0.260   -0.387    1.833 
   1.399   -0.446   -0.716 
main: matrix AA^-1, should be 1:
   1.000   -0.000   -0.000 
   0.000    1.000    0.000 
  -0.000   -0.000    1.000 
main: matrix A^-1A, should be 1:
   1.000    0.000    0.000 
  -0.000    1.000   -0.000 
  -0.000   -0.000    1.000