Kernel vector of statics Jacobian

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SUMMARY

The discussion centers on calculating the kernel vector of a 3x3 statics Jacobian. The original method involves removing a column from the Jacobian to create a 3x4 matrix, but this approach is invalid as it leads to a non-square matrix, making determinant calculation impossible. Participants suggest exploring alternative methods to find the kernel vector without removing a column. Clarification on the specific representation of the column vector and its relevance to statics in physics is also requested.

PREREQUISITES
  • Understanding of statics Jacobians in physics
  • Knowledge of linear algebra concepts, specifically determinants
  • Familiarity with kernel vectors in mathematical contexts
  • Basic proficiency in matrix operations
NEXT STEPS
  • Research methods for calculating kernel vectors without altering matrix dimensions
  • Study the implications of non-square matrices in linear algebra
  • Explore alternative representations of statics Jacobians
  • Investigate the application of kernel vectors in physics problems
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This discussion is beneficial for students and professionals in physics, particularly those dealing with statics, as well as mathematicians and engineers focused on linear algebra and matrix theory.

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Hi all,

I was reading an article that utilized a 3x4 statics Jacobian and said to calculate the kernel vector:
QVXCwFd.png
You can row by row, where
L6af21V.png

Where Ai is the statics Jacobian with the ith column removed. The problem is I have a 3x3 statics Jacobian, so if I remove the ith column I will end up with a non-square matrix, which means taking the determinant would not be possible. Is there another way to find the kernel vector in a similar way? Could I not remove the column?

Thanks!
 
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You are using specialized terminology and it's unclear what your column vector represents. It would help if you gave a link to the article you mention or show a relevant passage from it. Are you working a problem in "statics", as in physics?
 

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