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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?

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-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

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  • $\begingroup$ Fair point. It still intrigues me as to why -(1/6)*1+(1/3)*(1/2) still comes out as an actual 0, and not -2.776D-17. As if the internal "black box" approximations of rational numbers weren't the same in both cases. $\endgroup$ – James Well Nov 8 at 18:03
  • $\begingroup$ @JamesWell it's likely that the inverse operation has some error and that it doesn't return exactly 1/6 and 1/3. From pure floating point math with those values, you should get zero exactly. $\endgroup$ – Tyberius Nov 12 at 3:30

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