How to make the inverse operation of a " \ " operator ?

Lets have a square matrix A, and a rectangular transformation X, such that B has a lower order than A and one has the following expresion:

B=(X\A)*X;

If experimentally somehow One alreaddy has the datta from both B and X, how to solve the expresion for A without using pinv(X)? (wich actually is not accurrate)

[Jan]

Why do you assume that the PINV method is not "accurate"?

[Carlos A. Morales Rergis]

well actually I've tried, knowing A and X, and finding an experimental approximation to B, the fact is that rebuilding A with that datta and assuming that there are no messuarement mistakes the reconstruct datta does not match in any sense with its original set.

Anyway... perhaps in order to have a both sides transform use a sentence like B=pinv(X)*A*X;

the fact is that because of the size of the matrixes matlab itself recomends instaed of pinv(X) the use of " \ " operator...

what i mean is that I cannot mix both of the "pinv" and " \ " am i right??

Answer 1

[Roger Stafford]

In general there will not be enough information to deduce A from B and X. Consider the simple case where B is 1 x 1, X is 2 x 1, and the unknown A is 2 x 2. The matrix equality Y = X\A is overdetermined and has a least squares solution which yields two equations, and the matrix equality Y*X = B will yield only one further equation. This gives three equations and six unknowns for Y and A, which are certainly not sufficient to determine the four unknown elements of A.