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Re: fast matrix determinant

Newsgroups comp.lang.forth
Date 2017-06-16 06:04 -0700
References (7 earlier) <ohu72p$nob$1@dont-email.me> <1435c2f6-0633-4ed3-9dd1-e68d30442114@googlegroups.com> <oi00ml$lab$1@dont-email.me> <cc86be22-56e3-4816-9a13-517ec5f2af9c@googlegroups.com> <oi0ked$l1f$1@dont-email.me>
Message-ID <703dcda2-bf63-4889-afef-aadd7b77f3db@googlegroups.com> (permalink)
Subject Re: fast matrix determinant
From krishna.myneni@ccreweb.org

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On Friday, June 16, 2017 at 7:58:17 AM UTC-5, hum9 wrote:
...
> Inside proof, it was demonstrated that left side of equality 4) is zero:
> 
> for every k=1..N
> 
>      ([A] -Lk*[I]) * {dx}k = 0
> 
> That means delta-eigenvector {dx}k is also an eigenvector of [A]!
> 

The eigenvectors of A' = A + dA cannot be exact eigenvectors of A, in general. You are assuming this as an approximation to obtain the first-order corrections to the eigenvalues of A. Please look up perturbation theory, and, in particular, first-order perturbation theory.

Krishna

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fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-10 10:29 -0700
  Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-12 05:41 -0700
    Re: fast matrix determinant mhx@iae.nl - 2017-06-12 06:03 -0700
      Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-12 07:14 -0700
        Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-12 07:28 -0700
        Re: fast matrix determinant mhx@iae.nl - 2017-06-12 11:21 -0700
          Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-12 16:39 -0700
        Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-14 18:05 +0300
          Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-14 11:05 -0700
            Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-14 21:37 +0300
          Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-15 09:59 +0300
            Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-15 03:30 -0700
              Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-15 17:57 +0300
                Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-15 19:06 -0700
                Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-16 10:21 +0300
                Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-16 03:38 -0700
                Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-16 15:58 +0300
                Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-16 06:04 -0700
                Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-16 16:19 +0300
                Re: fast matrix determinant mhx@iae.nl - 2017-06-16 03:58 -0700
                Re: fast matrix determinant albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-06-16 13:39 +0200
                Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-16 05:58 -0700
                Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-16 05:12 -0700
                Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-16 05:40 -0700
                Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-16 17:50 +0300
                Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-16 13:39 -0700
                Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-17 10:01 +0300
                Re: fast matrix determinant mhx@iae.nl - 2017-06-17 01:31 -0700
                Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-17 15:24 -0700
            Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-15 17:59 +0300
          Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-16 10:11 +0300
            Re: fast matrix determinant hum9 <obi65537@gmail.com> - 2017-06-17 09:20 +0300
      Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-13 16:43 -0700
        Re: fast matrix determinant mhx@iae.nl - 2017-06-13 22:04 -0700
        Re: fast matrix determinant mhx@iae.nl - 2017-06-14 12:23 -0700
          Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-14 18:31 -0700
    Re: fast matrix determinant krishna.myneni@ccreweb.org - 2017-06-15 19:13 -0700

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