Determinant of the Jacobian

Sorry i cant help but could you explain to me what a Jacobian-Matrix is. Sounds interesting

leeps wrote: [...]

The determinant is equal to the product of the eigenvalues, right?

Since A*B=I for B=A^(-1), each eigenvalue x of A has a corresponding eigenvalue y=1/x in B... (Incomplete argument, but the fact remains.)

Thus, as the determinant (product of the eigenvalues) increases in B, at least one of the eigenvalues in A must approach 0. Hence, A is approaching a singularity.

Now, that said and done, if your matrix A is nearly singular (determinant of B is high; that of A is nearly 0), then the numerically calculated inverse B will generally be "incorrect" and virtually worthless. Thus, why don't you just monitor the determinant of A itself, and only calculate the inverse B when it is numerically stable?

Maybe I'm missing something in your application?

Later, Daniel

P.S. I'm not monitoring the newsgroup closely...