Comments on: Simultaneous Diagonalization of Hermitian Matrices

By: shahab

shahab — Tue, 27 Apr 2010 16:09:51 +0000

I see…
thanks.

By: Kabam_101

Kabam_101 — Wed, 07 Apr 2010 23:12:15 +0000

@shahab: I don’t see any trick on this. Everything is just fine. The eigenvectors were not just “chosen” but actually solved from the other matrix (\Lambda) which commutes with the matrix (\Omega) you wanted to diagonalize. The only important thing missing here is that it wasn’t mentioned that this method only works if both matrices commute.

By: shahab

shahab — Mon, 05 Apr 2010 22:53:16 +0000

well im not too sure but i think you have tricked us here….
in practice one doesnt happen to choose the values for the e’vectors of the degenerate matrix that fits the other one…!

By: Chen Feng

Chen Feng — Thu, 10 Dec 2009 20:54:15 +0000

Hello, MARYJANE. I just want to point out that the simultaneous denationalization works here because your matrices commute (\Omega \Gamma = \Gamma \Omega). In general, we can’t simultaneously diagonalize two matrices. Please refer to page 235 of the book ‘Matrix Analysis’ by Horn R A. And email me if you want to discuss more about this important research issue.

By: catherine therese quiñones

catherine therese quiñones — Fri, 14 Aug 2009 13:43:08 +0000

Hi ate MJ! Thanks for that article. It’s very informative indeed! However, I noticed some clerical errors but anyway the important thing is that you presented it in a manner that newbies could understand.

By: Hananish Joy

Hananish Joy — Tue, 11 Aug 2009 06:19:47 +0000

I don’t mean that you made an effort to make the minimal errors…hahaha…

what i mean is thank you for the effort of showing the process on simultaneous diagonalization. This will reslly help a lot in our xeam.

Thanks again:).

By: Hananish Joy

Hananish Joy — Tue, 11 Aug 2009 06:17:11 +0000

The process on diagonalizing the two hermitian matrices was presented in a way that the reader could understood. The minimal errors encourage me to really study the topic well. Thanks for the effort.

By: Gibson T. Maglasang

Gibson T. Maglasang — Thu, 06 Aug 2009 04:11:42 +0000

Good day to you ate MJ. Thanks to this article, it really cultivated me to love and appreciate hermitian operators because of its elegance and for being a special operator. Although there were minimal errors on the sign along the calculations but its acceptable for me.

Congratulations!

By: Sandra L. Manulat

Sandra L. Manulat — Thu, 06 Aug 2009 04:05:18 +0000

The simultaneous diagonalization of hermitian matrices would have been perfect if there weren’t any mistakes on the matrix elements and eigenvalues. Although these were just clerical errors but these could cause confusion especially to those who are new to this subject. Thank You!

By: Majvell Kay Odarve

Majvell Kay Odarve — Thu, 06 Aug 2009 04:02:00 +0000

Hello Ms. Mary Jane. I find your article very informative. I have really learned the basic steps on how to simultaneously diagonalize two Hermitian matrices. I only have a question though on what is your basis in selecting the values for the arbitrary variables? It seems that the Gram-Schmidt procedure for acquiring orthogonal vectors was not performed. How can I be sure that the values of the variables I selected are already orthogonal? thank you so much and more power.