From: Jamet
Subject: matrix inversion  in TLisp
Date: 
Message-ID: <94b35eee.0111120726.3a960bde@posting.google.com>
Hi,

i'm working with a neural network simulator. The programing language
is the TLisp. I'm searching a code for inversing a matrix mxn. Can
someone help me?

Thank you,
Cedric Jamet

From: Steve Long
Subject: Re: matrix inversion  in TLisp
Date: 
Message-ID: <3BF08D5F.B6C5F26D@isomedia.com>
CJ,

Is your "matrix" an array, vector, or list?

SL

Jamet wrote:

> Hi,
>
> i'm working with a neural network simulator. The programing language
> is the TLisp. I'm searching a code for inversing a matrix mxn. Can
> someone help me?
>
> Thank you,
> Cedric Jamet
From: Jamet
Subject: Re: matrix inversion  in TLisp
Date: 
Message-ID: <656ab2ce.0111140035.2f9e4521@posting.google.com>
Steve Long <·········@isomedia.com> wrote in message news:<·················@isomedia.com>...

> CJ,

> 

> Is your "matrix" an array, vector, or list?

> 

> SL



My matrix is an array mxn. I found code for square matrix but not for mxn matrix.
From: Michael A. Koerber
Subject: Re: matrix inversion  in TLisp
Date: 
Message-ID: <3BF27185.6872561B@ll.mit.edu>
Jamet wrote:

> My matrix is an array mxn. I found code for square matrix but not for mxn matrix.

There are three possibilities for the problem as stated:

1.  A is an MxN matrix with M=N...we all know the answer.  If A is
invertible,       use a Gaussian method to solve Ax = b.  If A is not
invertible consider a        minimum norm solution (below).

2.  A is MxN with M > N.  This is the over constrained Least Squares
problem.
    Given we desire a solution to Ax = b, do this...

    A^H A x = A^H b
    x 'approx' (A^H A)\ (A^H b)

    where A^H is the Hermetian transpose of A (I assumed A was complex,
    if A is real, just use a transpose).  Similar to 1, invertibility 
    is assumed; this time in (A^H A)

3.  A is MxN with M < N.  This is an under contrained case for which you 
    have an infinity of solutions or no solutions.  To get control over 
    this problem add a minimum-norm constraint.  See Golub & Van Loan,
    "Matrix Computations", pg 256--258.  You'll need QR decomp or SVD 
    routines.

NOW...if it is just the inverse that is needed and NOT a solution for x
as I assumed above, read about the Moore-Penrose inverse (G&VL pg 243).

I hope this helps.

mike


-- 
-------------------------------------------------------------------
Dr Michael A. Koerber       We child proofed our home 3 years ago 
MIT/Lincoln Laboratory      and they're still getting in!         
···@ll.mit.edu
From: ROHNE Ole
Subject: Re: matrix inversion  in TLisp
Date: 
Message-ID: <ebwzo5ppu5m.fsf@suntrt2.cern.ch>
············@lodyc.jussieu.fr (Jamet) writes:

> My matrix is an array mxn. I found code for square matrix but not
> for mxn matrix.

Please tell us if you do find code to invert non-square matrices -
most people think it's impossible (even in lisp:-) You might consider
a Least-Squares solution...

	Ole

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