# Determinant of the Jacobian

Hello I am working with a hexapod-robot having stewart-gough-platform.
Question: We are using the determinant of the (inverted) Jacobian-Matrix
as a criteria for avoiding singularities while moving. From my predecessor, I am using some software tool with defined limits to prevent any singularities. Lets say a value of the determinant of "14000", what does it mean and how should this value be evaluated?
Thanks for any help
Pierre
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Pierre wrote:

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

<http://en.wikipedia.org/wiki/Jacobian_matrix
--
http://www.flexusergroup.com /

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Pierre 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...
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