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MathGroup Archive 2005

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Re: Diagonalizing a non-Hermitian Matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58772] Re: Diagonalizing a non-Hermitian Matrix
  • From: AES <siegman at stanford.edu>
  • Date: Sun, 17 Jul 2005 13:03:19 -0400 (EDT)
  • Organization: Stanford University
  • References: <dbd0d3$2ni$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

If you're working with non-Hermitian matrices, you may need to dig into 
the concepts of adjoint matrices and adjoint eigenvalues; 
biorthogonality; "nonnormal systems" and "nonnormal modes"; and 
associated concepts.

There are some interesting physical problems in optics and quantum 
mechanics that involve non-Hermitian (sometimes also labelled 
"nonnormal") operators and their associated "nonnormal modes".

I'm no world-renowned expert on this subject, but

<http://www.stanford.edu/~siegman/nonnormal_modes_tamu_2003.pdf>

is a 500K PDF-format presentation that will introduce some of the basic 
concepts.


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