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:[email protected]] On Behalf Of Samuel Gougeon Sent: Monday, May 21, 2018 3:46 PM To: International users mailing list for Scilab. <[email protected]> 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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