Re: DiagonalizableQ

• To: mathgroup at smc.vnet.net
• Subject: [mg122107] Re: DiagonalizableQ
• From: "Hans Michel" <hmichel at cox.net>
• Date: Fri, 14 Oct 2011 05:53:57 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110130748.DAA02360@smc.vnet.net>

```There is no Mathematica built-in function called " DiagonalizableQ"
It is defined (constructed) just above "DiagonalizableQ[{{0, 1}, {0, 0}}]"
example as

DiagonalizableQ[m_?MatrixQ /; Apply[Equal, Dimensions[m]]] :=
Module[{s, j},
{s, j} = JordanDecomposition[m];
Length[
Cases[ArrayRules[j][[1 ;; -2, 1]], {i_, j_} /; j == i + 1]] == 0
];

Hans
-----Original Message-----
From: Jim Kochanski [mailto:jwkochanski at vcu.edu]
Sent: Thursday, October 13, 2011 2:48 AM
To: mathgroup at smc.vnet.net
Subject: [mg122107] DiagonalizableQ

When I cut and paste "DiagonalizableQ[{{0, 1}, {0, 0}}]"

>From the following, which can be found under Applications at
http://reference.wolfram.com/mathematica/ref/JordanDecomposition.html...

>> Test if a particular matrix is diagonalizable:
>> In[2]:= DiagonalizableQ[{{0, 1}, {0, 0}}]
>> Out[2]= False

I get... Out[2]= DiagonalizableQ[{{0, 1}, {0, 0}}] and not False

Can anyone give me some direction on using DiagonalizableQ?

Thanks!

Sincerely,

Jim

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James W. Kochanski
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```

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