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Re: Left eigenvector of generalized eigenvalue problem

• To: mathgroup at smc.vnet.net
• Subject: [mg76887] Re: [mg76860] Left eigenvector of generalized eigenvalue problem
• From: Carl Woll <carlw at wolfram.com>
• Date: Tue, 29 May 2007 05:02:34 -0400 (EDT)
• References: <200705280912.FAA19327@smc.vnet.net> <465ADEDA.5070007@wolfram.com> <4b15baf10705281343x70580c3ejd986137041d94536@mail.gmail.com>

Hussain AlQahtani wrote:

> Dear Carl
> Thansk for the prompt reply.
> Eigenvalues[{A,B}] gives the right eigenvector, however, I am 
> interested in calcualating the left eigenvector.
>  
> Thanks,

According to Mathematica's help:

The generalized eigenvalues of m with respect to a are those lambda for
which m.v == lambda a.v.

Isn't this the exact same equation as you have listed? Did you mean you
were interested in the eigenvalue problem

x . A == lambda x . B

instead of what you wrote? If so, can't you just use
Eigenvalues[Transpose /@ {A, B}]?

Carl Woll
Wolfram Research

>  
> On 5/28/07, *Carl Woll* <carlw at wolfram.com <mailto:carlw at wolfram.com>> 
> wrote:
>
>     KFUPM wrote:
>
>     >Dear group members,
>     >
>     >I am wondering how to compute the LEFT eigenvector of the
>     GENERALIZED
>     >eigenvalue problem:
>     >
>     >A x = lambda B x
>     >
>     >Thanks in anticipation for prompt reply.
>     >
>     >Regards,
>     >
>     >
>     >
>     Try
>
>     Eigenvalues[{A, B}]
>
>     Carl Woll
>     Wolfram Research
>
>
>
>
> -- 
> Hussain Al-Qahtani, Ph.D.
> Assistant Professor
>
> Department of Mechanical Engineering
> King Fahd University of Petroleum and Minerals
> P.O. Box 414 Dhahran, 31261
> Saudi Arabia
>
> 966-3-860-2864 (Office)
> 966-3-860-2949 (Fax)
>

• References:
  • Left eigenvector of generalized eigenvalue problem
    • From: KFUPM <hussain.alqahtani@gmail.com>