Which is the Correct Jordan Form?

[arthurhenry]

In the book I am looking only one of the following is listed as a Jordan Form. Could somebody tell me why the other one is not (that is, if I were confused again, which property of a Jordan Form I should check and decide on the correct one)
Thank you

210 200
020 021
002 002

 

[micromass]

Hi arthurhenry!

Those both look like Jordan forms to me. Did the book specifically say that the other one wasn't a Jordan form?

 

[HallsofIvy]

It is possible that, in order to make the "Jordan Form" unique", your textbook is requiring that "Jordan blocks" come before "isolated" eigenvectors. But that is not standard.

 

[Zorba]

It is possible that, in order to make the "Jordan Form" unique", your textbook is requiring that "Jordan blocks" come before "isolated" eigenvectors. But that is not standard.

That sounds about right.

Look at the definition in your book of a Jordon block matrix, does he say anything about the placement of Jordan blocks according to their multiplicities?

 

[arthurhenry]

Sorry for the late response, and I thank you all. Yes, I did find such a convention in the book.
So this should mean that I can show those two Jordan Forms are "the same", similar ?
I will try to show that now.
Thank you

 

[Zorba]

Yes, because if you rearrange the Jordan blocks, then you just have to rearrange the corresponding eigenvectors in the similiarity matrix, so this definition where he requires the Jordan blocks to be placed in a certain order is a bit stupid for this exact reason.

Fine, if it lends itself to a certain formalism but he should have made it clear in the text that the order does not matter, and by setting this question, he clearly has failed to do so.