[Scilab-users] det([]) changed in Scilab 6.0
Rafael Guerra
jrafaelbguerra at hotmail.com
Mon May 21 20:25:20 CEST 2018
Hi Samuel,
I am not a mathematician but I suspect that determinant rules you have enunciated do not hold for empty matrices.
Fyi, the following Wikipedia’s entry states that det([]) should be 1 (see ‘Empty matrices’ paragraph):
https://en.wikipedia.org/wiki/Matrix_(mathematics)#Empty_matrices
Regards,
Rafael
From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of Samuel Gougeon
Sent: Monday, May 21, 2018 2:10 PM
To: International users mailing list for Scilab. <users at lists.scilab.org>
Subject: [Scilab-users] det([]) changed in Scilab 6.0
Hello,
While updating "help empty" after changes in Scilab 6 about inequality comparisons with [],
i have found that det([]) is changed:
* 5.5: det([]) => 1
* 6.0: det([]) => 0
I don't know if this modification is intentional.
I am wondering about the added value of this change:
* If we consider the property for square matrices A & B:
det(A*B) = det(A)*det(B) (1)
setting det([])=0 better complies with it. Indeed, since []*B => [],
we have now det([]*B) = det([])*det(B) = 0*k = 0 = det([]) : OK
* In another hand, we should also have :
det(1/A) = 1/det(A) (2)
Since inv([]) => [], setting det([]) => 1 complied with (2),
while det([]) => 0 no longer does it.
Setting det([]) => [] would comply with both (1) and (2).
Let's note that Octave returns 1.
So, shall we restore det([]) ==1, or keep 0, or set it to [] ?
What's the improvement in changing det([]) to 0 ?
Regards
Samuel
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