What's relation between factorial and tensor components.?

In summary, the conversation discusses the use of permutation and combination techniques, as well as factorials of independent components of tensor curl and Levi-Civita, in relation to pseudo-tensors and tensor density. The use of factorials is seen as an artifact of using summation conventions, and the Levi-Civita tensor represents the unit pseudoscalar in space.
  • #1
aditya23456
114
0
maybe its simple permutation and combination technique... I ve tried to resolve it on my own but I couldn't...The textbook which I read simply mentions it to be obvious..can anyone please elucidate me the logic behind factorials of "independent components of tensor curl" and levi cita

Can anyone also explain the relation between pseudo-tensor and tensor density.?(with practical example hopefully)
 
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  • #2
can anyone please help me
 
  • #3
What specifically are you are asking? Your post doesn't provide enough detail.
 
  • #4
In dual tensors,levi ceta symbols we have some factorials..how are they assigned.?
 
  • #5
It's just an artifact of using summation conventions. Levi-Civita in N dimensions generally has [itex]1/N![/itex] appear somewhere.

Realizing that the Levi-Civita tensor represents the unit pseudoscalar in the space obviates the need for factorials.
 

Related to What's relation between factorial and tensor components.?

1. What is a factorial?

A factorial is a mathematical function denoted by the symbol "!", which represents the product of all positive integers from 1 up to a given number. For example, 5! (read as "five factorial") is equal to 1 x 2 x 3 x 4 x 5 = 120.

2. What is a tensor?

A tensor is a mathematical object that can be represented as a multi-dimensional array of numbers. It is used in various fields of science and engineering to describe physical quantities and their relationships.

3. How is factorial related to tensor components?

In mathematics, factorial is used to calculate the number of ways in which a set of objects can be arranged. Similarly, tensor components represent the different ways in which a tensor can be expressed in a coordinate system. The number of components in a tensor is equal to the factorial of the dimension of the tensor.

4. Can tensors be expressed using factorials?

Yes, in some cases, tensors can be expressed using factorials. For example, the permutation tensor, which is used to represent rotations in physics, can be written in terms of factorials.

5. What is the significance of the relation between factorial and tensor components?

The relation between factorial and tensor components is important in understanding the structure and properties of tensors. It also helps in simplifying calculations and making connections between different fields of mathematics and science.

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