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

[Rafael Guerra]

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



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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