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:[email protected]] *On Behalf Of
*Samuel Gougeon
*Sent:* Monday, May 28, 2018 12:09 AM
*To:* Users mailing list for Scilab <[email protected]>
*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
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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
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