[Scilab-users] Is cond([]) 0 or 1 ? (bug 15579)

[philippe]

Le 21/05/2018 à 15:46, Samuel Gougeon a écrit :
> 
> There are at least two way to do it :
> 
>   * either keep *cond([])* to *1* and set all *cond([], p)* to 1 instead
>     of 0
>   * or set *cond([])* to *0*.
> 
> I don't see any clear reason enforcing a choice rather than the other.
> Do you?

from a mathematical point of view  the Condition number of a matrix A is
defined by

cond(A)=||A|| . ||A^(-1)||
its interest is that when solving A*x=y rounding errors on y (eps) are
amplified to be cond(A)*eps. The optimal value of cond(A) is 1 (for
identity matrix) so for me it looks natural that cond([])=1 .

Philippe