# Re: JordanDecomposition trouble

• To: mathgroup@smc.vnet.net
• Subject: [mg10703] Re: JordanDecomposition trouble
• From: Paul Abbott <paul@physics.uwa.edu.au>
• Date: Fri, 30 Jan 1998 04:24:38 -0500
• Organization: University of Western Australia
• References: <6ahmmp\$pfa@smc.vnet.net>

```Josip Loncaric wrote:

> Let {s,j} denote Jordan decomposition of the following exact matrix:
>
> m = {{0,1,0,1},{0,0,0,0},{0,1,0,1},{0,0,0,0}}
> {s,j} = JordanDecomposition[m]
>
> We should have m == s.j.Inverse[s], but in Mathematica 3.01 this is not
> the case.
> Instead, we get a rather different result:
>
> In[3]:= s.j.Inverse[s]
> Out[3]= {{0,1,0,2},{0,0,0,0},{0,1,0,2},{0,0,0,0}}
>
> The problem is not in matrix inversion since s.Inverse[s] returns
> identity.  The source of trouble appears to be in the
> JordanDecomposition result.

Certainly looks that way.  Since Jordan decomposition works with
symbolic parameters, looking at

In[1]:= m = {{0, 1, 0, 1}, {0, 0, 0, 0}, {0, 1, 0, 1}, {0, 0, 0, a}};

In[2]:= {s, j} = JordanDecomposition[m]

In[3]:= s.j.Inverse[s]==m
Out[3]= True

In[4]:= s
Out[4]=
1                            1
{{0, 1, 0, -}, {0, 0, 1, 0}, {-1, 1, 0, -}, {0, 0, 0, 1}}
a                            a

may give a hint as to why the Jordan decomposition failed.

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907
mailto:paul@physics.uwa.edu.au  AUSTRALIA
http://www.pd.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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