what does it mean to be symmetric for tensors and Kronecker delta symbols and help explain this answer to me
i understand how to change 2 tensors into Kronecker delta symbols but unsure how they managed to transform back to just one. If someone could add all the steps to get to the answer that would be amazing :)
tensor-products tensors tensor-decomposition kronecker-delta
asked Nov 27 at 17:23
complexityyy
407
add a comment |
i understand how to change 2 tensors into Kronecker delta symbols but unsure how they managed to transform back to just one. If someone could add all the steps to get to the answer that would be amazing :)
tensor-products tensors tensor-decomposition kronecker-delta
asked Nov 27 at 17:23
complexityyy
407
Do you know about (anti)symmetric matrices?
– hkBst
Nov 27 at 17:30
no but I do know about matrices in general
– complexityyy
Nov 27 at 17:53
add a comment |
i understand how to change 2 tensors into Kronecker delta symbols but unsure how they managed to transform back to just one. If someone could add all the steps to get to the answer that would be amazing :)
tensor-products tensors tensor-decomposition kronecker-delta
asked Nov 27 at 17:23
complexityyy
407
i understand how to change 2 tensors into Kronecker delta symbols but unsure how they managed to transform back to just one. If someone could add all the steps to get to the answer that would be amazing :)
tensor-products tensors tensor-decomposition kronecker-delta
tensor-products tensors tensor-decomposition kronecker-delta
asked Nov 27 at 17:23
complexityyy
407
asked Nov 27 at 17:23
complexityyy
407
asked Nov 27 at 17:23
complexityyy
407
asked Nov 27 at 17:23
complexityyy
407
asked Nov 27 at 17:23
complexityyy
407
407
Do you know about (anti)symmetric matrices?
– hkBst
Nov 27 at 17:30
no but I do know about matrices in general
– complexityyy
Nov 27 at 17:53
add a comment |
Do you know about (anti)symmetric matrices?
– hkBst
Nov 27 at 17:30
no but I do know about matrices in general
– complexityyy
Nov 27 at 17:53
Do you know about (anti)symmetric matrices?
– hkBst
Nov 27 at 17:30
Do you know about (anti)symmetric matrices?
– hkBst
Nov 27 at 17:30
no but I do know about matrices in general
– complexityyy
Nov 27 at 17:53
no but I do know about matrices in general
– complexityyy
Nov 27 at 17:53
add a comment |
1 Answer
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By the replacement property:
begin{align*}
(delta_{ad}delta_{be}-delta_{ae}delta_{bd})varepsilon_{efa}
&=delta_{ad}delta_{be}varepsilon_{efa}-delta_{ae}delta_{bd}varepsilon_{efa} \
&=delta_{be}varepsilon_{efd}-delta_{bd}varepsilon_{afa} \
&=varepsilon_{bfd}-0,
end{align*}
since, if an index is repeated, the Levi-Civita symbol is zero.
answered Nov 27 at 17:30
Adrian Keister
4,77351933
thank you so much!
– complexityyy
Nov 27 at 17:52
You're welcome!
– Adrian Keister
Nov 27 at 17:54
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
By the replacement property:
begin{align*}
(delta_{ad}delta_{be}-delta_{ae}delta_{bd})varepsilon_{efa}
&=delta_{ad}delta_{be}varepsilon_{efa}-delta_{ae}delta_{bd}varepsilon_{efa} \
&=delta_{be}varepsilon_{efd}-delta_{bd}varepsilon_{afa} \
&=varepsilon_{bfd}-0,
end{align*}
since, if an index is repeated, the Levi-Civita symbol is zero.
answered Nov 27 at 17:30
Adrian Keister
4,77351933
thank you so much!
– complexityyy
Nov 27 at 17:52
You're welcome!
– Adrian Keister
Nov 27 at 17:54
add a comment |
By the replacement property:
begin{align*}
(delta_{ad}delta_{be}-delta_{ae}delta_{bd})varepsilon_{efa}
&=delta_{ad}delta_{be}varepsilon_{efa}-delta_{ae}delta_{bd}varepsilon_{efa} \
&=delta_{be}varepsilon_{efd}-delta_{bd}varepsilon_{afa} \
&=varepsilon_{bfd}-0,
end{align*}
since, if an index is repeated, the Levi-Civita symbol is zero.
answered Nov 27 at 17:30
Adrian Keister
4,77351933
thank you so much!
– complexityyy
Nov 27 at 17:52
You're welcome!
– Adrian Keister
Nov 27 at 17:54
add a comment |
By the replacement property:
begin{align*}
(delta_{ad}delta_{be}-delta_{ae}delta_{bd})varepsilon_{efa}
&=delta_{ad}delta_{be}varepsilon_{efa}-delta_{ae}delta_{bd}varepsilon_{efa} \
&=delta_{be}varepsilon_{efd}-delta_{bd}varepsilon_{afa} \
&=varepsilon_{bfd}-0,
end{align*}
since, if an index is repeated, the Levi-Civita symbol is zero.
answered Nov 27 at 17:30
Adrian Keister
4,77351933
By the replacement property:
begin{align*}
(delta_{ad}delta_{be}-delta_{ae}delta_{bd})varepsilon_{efa}
&=delta_{ad}delta_{be}varepsilon_{efa}-delta_{ae}delta_{bd}varepsilon_{efa} \
&=delta_{be}varepsilon_{efd}-delta_{bd}varepsilon_{afa} \
&=varepsilon_{bfd}-0,
end{align*}
since, if an index is repeated, the Levi-Civita symbol is zero.
answered Nov 27 at 17:30
Adrian Keister
4,77351933
answered Nov 27 at 17:30
Adrian Keister
4,77351933
answered Nov 27 at 17:30
Adrian Keister
4,77351933
answered Nov 27 at 17:30
Adrian Keister
4,77351933
4,77351933
thank you so much!
– complexityyy
Nov 27 at 17:52
You're welcome!
– Adrian Keister
Nov 27 at 17:54
add a comment |
thank you so much!
– complexityyy
Nov 27 at 17:52
You're welcome!
– Adrian Keister
Nov 27 at 17:54
thank you so much!
– complexityyy
Nov 27 at 17:52
thank you so much!
– complexityyy
Nov 27 at 17:52
You're welcome!
– Adrian Keister
Nov 27 at 17:54
You're welcome!
– Adrian Keister
Nov 27 at 17:54
add a comment |
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Do you know about (anti)symmetric matrices?
– hkBst
Nov 27 at 17:30
no but I do know about matrices in general
– complexityyy
Nov 27 at 17:53