<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
</head>
<body bgcolor="#FFFFFF" text="#000000">
Hello,<br>
<br>
While updating "help empty" after changes in Scilab 6 about
inequality comparisons with [], <br>
i have found that det([]) is changed:
<ul>
<li>5.5: det([]) => 1</li>
<li>6.0: det([]) => 0</li>
</ul>
<p>I don't know if this modification is intentional.<br>
I am wondering about the added value of this change:</p>
<ul>
<li>If we consider the property for square matrices A & B: <tt><br>
det(A*B) = det(A)*det(B)</tt> (1)<br>
setting det([])=0 better complies with it. Indeed, since []*B
=> [],<br>
we have now det([]*B) = det([])*det(B) = 0*k = 0 = det([]) : OK<br>
<br>
</li>
<li>In another hand, we should also have :<br>
<tt>det(1/A) = 1/det(A)</tt> (2)<br>
Since inv([]) => [], setting det([]) => 1 complied with
(2),<br>
while det([]) => 0 no longer does it.</li>
</ul>
<p>Setting<tt> det([]) => [] </tt>would comply with both (1) and
(2).<br>
</p>
<ul>
</ul>
<p>Let's note that Octave returns 1.</p>
<p>So, shall we restore det([]) ==1, or keep 0, or set it to [] ?</p>
<p>What's the improvement in changing det([]) to 0 ?<br>
</p>
<p>Regards<br>
Samuel<br>
<br>
</p>
</body>
</html>