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The mysterious 2skew function...


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Hello,

Background:
I was going to implement an implicit approach to 3d tetrahedra deformations (first in Matlab then in C++).
I need the Jacobian for the partial derivative of force wrt position to do this.
I found this paper that gives a method for computing it:
http://www-bcf.usc.edu/~jbarbic/Barb...nessMatrix.pdf

The Question:
In the report, he defines a 2skew function (to the right of the page). I'm pretty confused on what it means. I think I forgot what skew means from linear algebra - that's probably part of my problem. It sounds like skew symmetric means that a negated matrix is equal to its transpose. What exactly is this 2skew function for?

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You have the notion of skewness and skew functions in statistics, but this is I think not what you are asking about.

 

I assume the author is talking about bilinear forms and/or matrices being skew symmetric.

 

It means that under the interchange of some indices we have A_{ij} =-A_{ji}.

 

For a bilinear form we have B(u,v) = - B(v,u).

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