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

 From: anonymous Subject: [Octave-bug-tracker] [bug #55256] Wrong result raise a non-diagonalizable matrix by a fractional exponent Date: Thu, 20 Dec 2018 14:54:03 -0500 (EST) User-agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:64.0) Gecko/20100101 Firefox/64.0

```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
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

_______________________________________________________

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

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