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-boun...@lists.scilab.org] On Behalf Of Samuel Gougeon Sent: Monday, May 21, 2018 2:10 PM To: International users mailing list for Scilab. <users@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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