Matrix multiplication not working in Scilab

Question

I entered an instruction to calculate the coordinates of a vector after a change of basis in order to repeat it many times with various vectors.

X0=[1;1/2] is a set of coordinates in the initial basis and P=[-4,2;1,1] is the new basis expressed in the initial one.

When I compute P^(-1)*X0 I get :

ans = [-2.776D-17 ; 0.5]

The problem is, when I work it out by hand, I get P^(-1)=[-1/6,1/3;1/6,2/3] which Scilab agrees with, and then the first coordinate of P^(-1)*X0 should be 0.

So I attempted to calculate that first coordinate manually with Scilab, by entering (-1/6)*1+(1/3)*(1/2) which indeed gave me 0 as an answer.

I tried restarting Scilab which didn't resolve the issue, and I'm not a computer expert, anyone seen this happen before?

Answer 1

-2.776D-17 equals $-2.776\cdot 10^{-17}$, which is indeed very small and for all practical purposes is zero. I think scilab is OK

Answer 2

In your example inv(P) is not equal to [-1/6,1/3;1/6,2/3]. The problem is that before 6.1 version, Scilab was sometimes displaying very small numbers as zero. In Scilab 6.0.2 and older versions, you will see (using recursive extraction allow to see actual non-zero term) :

--> P=[-4,2;1,1]; inv(P)-[-1/6,1/3;1/6,2/3]
 ans  =

   0.   0.
   0.   0.

--> (inv(P)-[-1/6,1/3;1/6,2/3])(1,1)
 ans  =

  -2.776D-17

In Scilab 6.1 the display is fully explicit:

--> P=[-4,2;1,1]; inv(P)-[-1/6,1/3;1/6,2/3]
 ans  =

  -2.776D-17   0.
   0.          0.