Re: don't understand inverseimage

[Bill Allombert <allomber@math.u-bordeaux.fr>]

On Thu, Dec 19, 2002 at 11:16:49AM +0100, Ramón Casero Cañas wrote:
> Bill Allombert wrote:
> > On Tue, Dec 17, 2002 at 11:10:42PM +0100, rcasero@tsc.uc3m.es wrote:
> 
> > matinverseimage(A,Y) return a solution of AX=Y if it exists, and [;] else.
> 
> Um, I have another question linked to Bill's answer. Let's say the 
> matrix is invertible. Each time that a vector's inverse image is to be 
> computed, the matrix has to be inverted (or whichever process it 
> follows), isn't it? That doesn't seem efficient from a computational 
> point of view (and I'm not saying that that function was written with 
> that idea, or maybe it's more efficient that way than inverting the 
> matrix and then use the inverse as a linear mapping, I don't know). I've 
> been reading other functions descriptions, and I haven't found anything 
> like "inverse(A)".

1) To inverse a matrix, use A^-1 or 1/A.

2) If A is invertible, you should rather use matsolve() than matinverseimage().

3) matsolve(A,X) is faster than computing A^-1, but not much, so you are right,
it is best to compute A^-1 if you have many vectors X.

Cheers,
Bill.