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<div class="moz-cite-prefix">Hello Philippe,<br>
<br>
Le 24/05/2018 à 23:20, philippe a écrit :<br>
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<blockquote cite="mid:pe7a7j$et5$1@blaine.gmane.org" type="cite">
<pre wrap="">Le 21/05/2018 à 15:46, Samuel Gougeon a écrit :
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<pre wrap="">
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?
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<pre wrap="">
from a mathematical point of view the Condition number of a matrix A is
defined by
cond(A)=||A|| . ||A^(-1)||
its interest is that when solving A*x=y rounding errors on y (eps) are
amplified to be cond(A)*eps. The optimal value of cond(A) is 1 (for
identity matrix) so for me it looks natural that cond([])=1 .</pre>
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<br>
I must confess that, unless claiming that <b><tt>norm([])</tt></b><b>
</b>is NOT 0, i do not catch clearly the logical of your conclusion
<br>
<ul>
<li><i>"The optimal value of cond(A) is 1 (for identity matrix) so
for me it looks natural that cond([])=1"</i></li>
</ul>
<p>Indeed, cond([]) = norm([])*norm(inv([])) = 0*norm([]) = 0*0 = 0<br>
</p>
<p>By the way, according to the clear explanation you give about the
meaning of the condition number, the value 0 is even more optimal:
it says that small variations are not getting amplified, but
killed.</p>
<p>Please let us know more about your proposal for 1 instead of 0.</p>
<p>Regards<br>
Samuel<br>
<br>
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