Cartesian Tensors and some proofs and problems regarding it.

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SUMMARY

The discussion centers on proving that the Kronecker delta is an isotropic tensor. Participants emphasize the necessity of understanding coordinate transformations to demonstrate that the Kronecker delta remains unchanged under these transformations. Key points include the definition of an isotropic tensor and the general method for transforming tensor components. The conversation highlights the importance of foundational knowledge in tensors for solving related problems.

PREREQUISITES
  • Understanding of isotropic tensors
  • Knowledge of coordinate transformations in tensor analysis
  • Familiarity with the Kronecker delta notation
  • Basic principles of tensor component transformation
NEXT STEPS
  • Study the definition and properties of isotropic tensors
  • Learn about coordinate transformation methods for tensors
  • Explore the application of the Kronecker delta in various tensor operations
  • Review examples of tensor component transformations in physics
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Students and researchers in physics and engineering, particularly those focusing on tensor analysis and its applications in mechanics and relativity.

Raj90
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Homework Statement



I am stuck at this point where I have to prove that the kronecker delta is isotropic tensor.

Homework Equations



δij=δji

The Attempt at a Solution


I know that to prove this I have to show that under coordinate transfor mation it does not change..but it's a bit diff for me to get it right...
 
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Raj90 said:
I have to prove that the kronecker delta is isotropic tensor.


I know that to prove this I have to show that under coordinate transfor mation it does not change.


Hi, Raj90. Welcome to PF.

You don't mean any coordinate transformation, right? What type of coordinate transformation are you assuming in order to show that the tensor is isotropic?

Do you know the general method for transforming tensor components from one system of coordinates to another?
 
Hey TSny!

No I am completely new to the subject..that is why I need some help and guidance as to what I should refer to solve the given problem.
 
You need to have some basic knowledge about tensors to solve the problem. We are here to help you once you have made an attempt and you show us your work so far. I will just say that for this problem you essentially need the following:

1. Know the definition of "isotropic tensor". This will tell you what type of coordinate transformation you need to consider.

2. Know the general method of transforming tensor components and apply this method to the specific type of coordinate transformation you are dealing with in this problem.
 

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