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

[anonymous]

URL:
  <https://savannah.gnu.org/bugs/?55256>

                 Summary: Wrong result raise a non-diagonalizable matrix by a
fractional exponent
                 Project: GNU Octave
            Submitted by: None
            Submitted on: Thu 20 Dec 2018 07:54:01 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: None
                  Status: None
             Assigned to: None
         Originator Name: Volker Becker
        Originator Email: address@hidden
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 4.4.1
        Operating System: Any

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Details:

If raise a non-diagonalizable matrix to a fractional power, the result is
wrong. 

For example:



>> A=[1 1 1; 0 1 1; 0 0 1]
A =

   1   1   1
   0   1   1
   0   0   1

>> B = A^0.5
B =

   1.00000   0.00000   0.00000
   0.00000   1.00000   0.00000
   0.00000   0.00000   1.00000

So B*B is obiously not equal to A. probaly the result will be calculated by
diagonalistion of the matrix which fails when the matrix is 
non-diagonalizable.

The correct result (due to wolfram aplha) would be 

C=[1 0.5 0.375; 0 1 0.5; 0 0 1]
C =

   1.00000   0.50000   0.37500
   0.00000   1.00000   0.50000
   0.00000   0.00000   1.00000

>> C*C
ans =

   1   1   1
   0   1   1
   0   0   1







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