Solving Tensor Problem: Need Help Now!

  • Thread starter Thread starter samson07
  • Start date Start date
  • Tags Tags
    Tensor
Click For Summary
SUMMARY

The discussion centers on the complexities of tensor notation and operations, specifically regarding the expression Aijkl=Fijkl(am). Aijkl represents a rank-4 tensor's components, while am denotes a vector. The confusion arises from the lack of explicit definitions for tensor operations such as A·B and A-1 in the context of four-index tensors. The participant concludes that F is a function that generates a rank-4 tensor from a six-parameter family of tensors, indicating a need for clarity in tensor algebra definitions.

PREREQUISITES
  • Understanding of tensor notation and operations
  • Familiarity with vector spaces and components
  • Knowledge of rank-4 tensors and their applications
  • Basic grasp of linear algebra concepts
NEXT STEPS
  • Research tensor algebra and its definitions
  • Study the properties of rank-4 tensors
  • Learn about tensor operations such as contraction and tensor products
  • Explore the implications of six-parameter families of tensors
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are dealing with tensor analysis and require a deeper understanding of tensor operations and notation.

samson07
Messages
3
Reaction score
0
Spent several hours in the library on this and i have no idea how to do...

please help I'm going to burst out with tears soon...
 

Attachments

  • 1.jpg
    1.jpg
    24.6 KB · Views: 464
Physics news on Phys.org
I can't make sense of any of that. Does Aijkl=Fijkl(am) mean that Aijkl is the result of letting Fijkl act on am? Then why doesn't A have five indices instead of four? Is am a vector or a component of a vector? Why doesn't m appear anywhere on the right? What are the definitions of A·B and A-1? (I haven't seen either defined for tensors with 4 indices). Does A denote the tensor and Aijkl its components in a coordinate system? Then what does A (no indices, not bold) denote?
 
Looks to me like F just takes a six-tuple of coefficients (what kind, who knows?) and spits out a rank-4 tensor. In other words, F is some six-parameter family of tensors. I suppose the answers will be in terms of the a_i's and b_i's (i=1,...,6).
 

Similar threads

How determine that a matrix is a tensor?
  • · Replies 19 ·
Replies
19
Views
3K
General relativity - Using Ricc and Weyl tensor to find the area
  • · Replies 1 ·
Replies
1
Views
2K
Finding the inverse of 4th rank elasticity tensor
  • · Replies 1 ·
Replies
1
Views
2K
I do not understand stress energy tensor for fluids
  • · Replies 6 ·
Replies
6
Views
3K
Derive the relationship between Ricci scalar and Gauss Curvature
  • · Replies 12 ·
Replies
12
Views
3K
Showing that the gradient of a scalar field is a covariant vector
  • · Replies 5 ·
Replies
5
Views
4K
Understanding the Maxwell Stress Tensor
  • · Replies 3 ·
Replies
3
Views
5K
Prove the well-established (in GR) stress-energy tensor formula
  • · Replies 4 ·
Replies
4
Views
2K
Showing that the Weyl tensor is invariant under conformal symmetries
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad How to calculate basis vectors from metric tensor (as a matrix)?
  • · Replies 6 ·
Replies
6
Views
1K