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Re: Diagonalizing

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  • Subject: [mg107210] Re: Diagonalizing
  • From: Bill Rowe <readnews at>
  • Date: Fri, 5 Feb 2010 03:25:14 -0500 (EST)

On 2/4/10 at 6:24 AM, lambaugh at (Jim Lambaugh) wrote:

>I am in a situation, where I have to diagonalize very large
>matrices. My experience with Mathematica is limited, but what I need
>is the entire set of eigenvalues. From what I have read, this
>excludes the use of ARPACK, since this is used to find certain
>eigenvalues (i.e. largest, smallest etc.).

>I read that LAPACK is used to find entire sets of eigenvalues, but
>the Mathematica-help does not say much on this subject. So to make a
>long story short: What is the most effective way of finding the
>entire set of eigenvalues (and corresponding eigenvectors) of a very
>large matrix?

Have you tried the built-in function Eigenvalues? My
understanding is the current version of Mathematica uses the
LAPACK library for many of its routines. And my guess is for an
arbitrary matrix you won't do any better than using the built-in
functions. Possibly for some specific cases, there might be a
faster more efficient method than using the built-in Eigenvalues function.

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