What is Vector Inversion and How Does It Differ from Vector Division?

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SUMMARY

The discussion centers on the concept of vector inversion, specifically addressing the mathematical operation of raising a vector to the power of negative one (V ^ (-1)). Participants clarify that traditional vector operations such as division or multiplicative inverses are not defined in vector mathematics, particularly emphasizing the limitations of the cross product, which is applicable only to three-dimensional vectors. The conversation highlights the complexity of vector operations and the need for a deeper understanding of vector algebra.

PREREQUISITES
  • Understanding of vector algebra
  • Familiarity with the cross product of vectors
  • Knowledge of three-dimensional geometry
  • Basic mathematical operations involving powers and inverses
NEXT STEPS
  • Research the properties and limitations of vector operations
  • Learn about the cross product and its applications in three-dimensional space
  • Explore advanced topics in linear algebra, focusing on vector spaces
  • Study the mathematical definitions of vector norms and inverses
USEFUL FOR

Mathematicians, physics students, and anyone studying vector algebra or looking to understand the complexities of vector operations.

jasper353
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How do you get a vector to the power of negative one?

I.E. : V ^ (-1)?

Or inversion if that's what it's called?

Thank you.
 
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I have never seen "division", or for that matter powers or products defined for vectors. Perhaps if you told us where you saw that and the situtation involved, we could say.

In edit: It has been pointed out to me that I forgot the "cross product" of vectors- but that is only defined for three dimensional vectors and still does not have multiplicative inverses defined.
 
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I see that it is more involved than I was hoping.

I followed the thread, and the other person is,

or was, having the same difficulty as I am or were.

Thanks :). Jasper.
 

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