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
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
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.
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
············@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
--