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

[Samuel Gougeon]

Le 27/05/2018 à 23:49, Rafael Guerra a écrit :
>
> You guys may have missed the paper sent before on the algebra of empty 
> matrices by Carl de Boor (Emeritus Professor in Mathematics and 
> Computer Science), so I am sending it again:
>
> https://pdfs.semanticscholar.org/0f3b/c36f19d5c6a761c19fbc3c4ebde2f31b0a10.pdf
>
> He argues that the condition number of the square empty matrix [] = 0 
> and its det([]) = 1
>

No no, i did not miss it. His argument is that norm([]) is 0:

/Any norm of an empty matrix is zero, as the supremum of the empty set 
of nonnegative numbers. This implies that the condition number of the 
square empty matrix [] is 0./

This does not prevent asking to Philippe why he proposes 1, noticeably 
if he also considers that norm([])==0, or not.

The De Boor argument "/as the supremum of the empty set of nonnegative 
numbers."/ is not clear to me./

/Is it clear for you? Would you have a second convergent independent 
reference?

Samuel

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