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

[Rafael Guerra]

Hi Samuel,

Please read the following article on this interesting topic of the algebra of empty matrices:
https://pdfs.semanticscholar.org/0f3b/c36f19d5c6a761c19fbc3c4ebde2f31b0a10.pdf

It states that the condition number of the empty matrix should be 0.

Regards,
Rafael

From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of Samuel Gougeon
Sent: Monday, May 21, 2018 3:46 PM
To: International users mailing list for Scilab. <users at lists.scilab.org>
Subject: [Scilab-users] Is cond([]) 0 or 1 ? (bug 15579)

Hello,

Another case with []:
The bug 15579<http://bugzilla.scilab.org/show_bug.cgi?id=15579> reports that cond([]) returns 1, while cond([],2) -- that computes the same 2-norm conditional number for any other matrix than [] -- returns 0.

Actually, cond([], p) returns 0 for any accepted p value.

At least since Scilab 4, and likely since the beginning of Scilab,  cond([]) is set to 1 as a specific case.
I am wondering why.

In my opinion, the mismatch between cond([]) and the equivalent cond([],2) must be fixed.
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?

Let's note that

  *   Octave returns 0 in both cond([]) and cond([],p) cases
  *   Julia, Python, and R (with kappa()) yield an error
Regards
Samuel
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