[Date Index] [Thread Index] [Author Index]

Re: Left eigenvector of generalized eigenvalue problem

• To: mathgroup at smc.vnet.net
• Subject: [mg76862] Re: Left eigenvector of generalized eigenvalue problem
• From: "Eckhard Hennig" <aidev at n-o-s-p-a-m.kaninkolo.de>
• Date: Tue, 29 May 2007 04:49:35 -0400 (EDT)
• References: <f3e6ie$it3$1@smc.vnet.net>

"KFUPM" <hussain.alqahtani at gmail.com> schrieb im Newsbeitrag 
news:f3e6ie$it3$1 at smc.vnet.net...
> Dear group members,
>
> I am wondering how to compute the LEFT eigenvector of the GENERALIZED
> eigenvalue problem:
>
> A x = lambda B x


A left eigenvector y satisfies the equation

  y* A = lambda y* B

where y* denotes the Hermitian conjugate (= complex conjugate transpose) of 
y.

Thus, y can be determined as right eigenvector of the Hermitian conjugate of 
the GEP:

  (A* - lambda B*) y = 0

Best regards,

Eckhard

--
Dr.-Ing. Eckhard Hennig
www.kaninkolo.de/ai
aidev \at kaninkolo \dot de