[Octave-bug-tracker] [bug #55256] Wrong result raise a non-diagonalizable matrix by a fractional exponent

[Rik]

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

Confirmed.

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 =

   6.3691e+15
   2.0282e+31
   2.0282e+31


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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