QR-factorisation via Givens rotations
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
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
R=(should be right-triangular)
    1.328    1.191    0.947
    0.000    0.621   -0.201
    0.000    0.000    0.433
Q*R= (should be equal the original 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
Q^T*Q= (should be equal identity matrix)
    1.000    0.000    0.000
    0.000    1.000   -0.000
    0.000   -0.000    1.000
Givens rotations: linear system
Random square 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
    0.365    0.513    0.952    0.916
Random right-hand-side b: 
    0.636    0.717    0.142    0.607
solution x to Ax=b      : 
    0.113   -1.142    0.272    0.975
check: Ax (should == b) : 
    0.636    0.717    0.142    0.607
Inverse matrix Ai =
    2.270   -0.317    0.231   -1.871
    1.588   -1.533    3.608   -2.576
    2.170   -1.803   -1.512    0.658
   -4.049    2.859   -0.542    2.596
Check: Ai*A (should == 1)
    1.000   -0.000    0.000   -0.000
    0.000    1.000    0.000    0.000
   -0.000    0.000    1.000    0.000
   -0.000   -0.000   -0.000    1.000
Check: A*Ai (should == 1)
    1.000    0.000    0.000    0.000
    0.000    1.000   -0.000    0.000
    0.000   -0.000    1.000    0.000
   -0.000    0.000    0.000    1.000