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Jordan Form

• To: mathgroup at smc.vnet.net
• Subject: [mg26310] Jordan Form
• From: "Matt Herman" <Henayni at hotmail.com>
• Date: Sun, 10 Dec 2000 21:37:56 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

I have found a bug in JordanDecomposition.

Consider the matrix A 
{
{2, 0, 0, 0, 0, 0, 0, 0},
{1, 2, 0, 0, 0, 0, 0, 0},
{-4, 1, 2, 0, 0, 0, 0, 0},
{2, 0, 0, 2, 0, 0, 0, 0},
{-7, 2, 0, 0, 2, 0, 0, 0},
{9, 0, -2, 0, 1, 2, 0, 0},
{-34, 7, 1, -2, -1, 1, 2, 0},
{145, -17, -16, 3, 9, -2, 0, 3}
}.

Then, Mathematica gives
In[3]:=
JordanDecomposition[A][[2]]
Out[3]=
{
{2, 1, 0, 0, 0, 0, 0, 0},
{0, 2, 0, 0, 0, 0, 0, 0},
{0, 0, 2, 1, 0, 0, 0, 0},
{0, 0, 0, 2, 0, 0, 0, 0},
{0, 0, 0, 0, 2, 1, 0, 0},
{0, 0, 0, 0, 0, 2, 1, 0},
{0, 0, 0, 0, 0, 0, 2, 0},
{0, 0, 0, 0, 0, 0, 0, 3}
}

Which is J(2,2)+J(2,2)+J(2,3)+J(3,1), where J(c,n) is the nxn matrix 
with c's on the diagonal, and ones on the upper (or lower) 
"subdiagonal".

However, if you do it by hand (i.e. computing nullspaces, etc..), you 
get that the JCF is J(2,3)+J(2,3)+J(2,1)+J(3,1), as confirmed by other 
systems. But the Jordan form is unique, so we have a problem.

Any ideas (and no, this is not a matter of not entering the matrix 
correctly)?