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

[Stéphane Mottelet]

Le 28/05/2018 à 10:58, Rafael Guerra a écrit :
>
> No, it is not clear but then, I am not an Emeritus Professor of 
> Mathematics.
>
> Sorry but I have no other references on this empty subject.
>
> Regards,
>
> Rafael
>
> *From:*users [mailto:users-bounces at lists.scilab.org] *On Behalf Of 
> *Samuel Gougeon
> *Sent:* Monday, May 28, 2018 12:09 AM
> *To:* Users mailing list for Scilab <users at lists.scilab.org>
> *Subject:* Re: [Scilab-users] Is cond([]) 0 or 1 ? (bug 15579)
>
> 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
>     <https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/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./
> /
>
Every property (even trivially false) is true for all elements of the 
empty set. Hence, any positive number can be taken as the supremum of 
the empty set. However, I don't see in which sense this could justify 
the discusses convention...

S.
>
> /
> /Is it clear for you? Would you have a second convergent independent 
> reference?
>
> Samuel
>
>
>
> _______________________________________________
> users mailing list
> users at lists.scilab.org
> https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users


-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.scilab.org/pipermail/users/attachments/20180528/befec8f8/attachment.htm>