what's relation between factorial and tensor components.?

aditya23456

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)

aditya23456

can anyone plz help me

Hurkyl

What specifically are you are asking? Your post doesn't provide enough detail.

aditya23456

In dual tensors,levi ceta symbols we have some factorials..how are they assigned.?

Muphrid

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.

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Hurkyl Recognitions: Gold Member Science Advisor Staff Emeritus	What specifically are you are asking? Your post doesn't provide enough detail.

aditya23456	what's relation between factorial and tensor components.? In dual tensors,levi ceta symbols we have some factorials..how are they assigned.?

Muphrid	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.