We expect mathematically that basiscoords A However if you

We expect, mathematically, that basis·coords = A. However, if you try the command A - (basiscoords) in MATLAB, you may not get all zeros. Why is this?

A = [-2 -2;1 3;0 4];

basis =

   -0.9195 -1.8874

1.2582 1.7773

1.5970 1.6672

coords =

   -2.2511 2.8456

2.1563 -0.3266

Solution

The cross product of basis x cords is orthogonal to both basis as well as cords. We can verify this by taking its dot product with both basis and cords. Remember, that the 2 vectors are orthogonal if and only if there dot product equals zero. This is the reason why we may not get all zeros.