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[Octave-bug-tracker] [bug #55256] Wrong result raise a non-diagonalizabl

From: Rik
Subject: [Octave-bug-tracker] [bug #55256] Wrong result raise a non-diagonalizable matrix by a fractional exponent
Date: Thu, 20 Dec 2018 20:13:08 -0500 (EST)
User-agent: Mozilla/5.0 (X11; Linux i586; rv:31.0) Gecko/20100101 Firefox/31.0

Follow-up Comment #1, bug #55256 (project octave):


If you calculate the condition number with respect to eig, you can see that
this is going to be a problem.

A=[1 1 1; 0 1 1; 0 0 1];
condeig (A)
warning: matrix singular to machine precision, rcond = 2.46519e-32
warning: called from
    condeig at line 94 column 8
ans =


Also, for grins, in this case one could use sqrtm rather than X^0.5 and that
functions succeeds.

sqrtm (A)
ans =

   1.00000   0.50000   0.37500
   0.00000   1.00000   0.50000
   0.00000   0.00000   1.00000

So, it looks like at a minimum Octave should warn when the matrix is
ill-conditioned and the results are unlikely to be accurate.


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