Multiple index repetition in Einstein notation
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My textbook says that $(X_1)^2 +(X_2)^2+(X_3)^2$ would be written $X_i cdot X_i$ in Einstein notation. It also says that you can only have 2 of the same index. But what if I wanted to express $(X_1)^3 +(X_2)^3+(X_3)^3$
Automatically, I would want to write $X_i cdot X_icdot X_i$, but this is not allowed.
Why does Einstein notation not allow an index to be repeated three times?
Is there some sort of ambiguity that it would cause?
tensors
asked Dec 24 '18 at 5:17
Ion SmeIon Sme
11510
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add a comment |
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My textbook says that $(X_1)^2 +(X_2)^2+(X_3)^2$ would be written $X_i cdot X_i$ in Einstein notation. It also says that you can only have 2 of the same index. But what if I wanted to express $(X_1)^3 +(X_2)^3+(X_3)^3$
Automatically, I would want to write $X_i cdot X_icdot X_i$, but this is not allowed.
Why does Einstein notation not allow an index to be repeated three times?
Is there some sort of ambiguity that it would cause?
tensors
asked Dec 24 '18 at 5:17
Ion SmeIon Sme
11510
$endgroup$
add a comment |
$begingroup$
My textbook says that $(X_1)^2 +(X_2)^2+(X_3)^2$ would be written $X_i cdot X_i$ in Einstein notation. It also says that you can only have 2 of the same index. But what if I wanted to express $(X_1)^3 +(X_2)^3+(X_3)^3$
Automatically, I would want to write $X_i cdot X_icdot X_i$, but this is not allowed.
Why does Einstein notation not allow an index to be repeated three times?
Is there some sort of ambiguity that it would cause?
tensors
asked Dec 24 '18 at 5:17
Ion SmeIon Sme
11510
$endgroup$
My textbook says that $(X_1)^2 +(X_2)^2+(X_3)^2$ would be written $X_i cdot X_i$ in Einstein notation. It also says that you can only have 2 of the same index. But what if I wanted to express $(X_1)^3 +(X_2)^3+(X_3)^3$
Automatically, I would want to write $X_i cdot X_icdot X_i$, but this is not allowed.
Why does Einstein notation not allow an index to be repeated three times?
Is there some sort of ambiguity that it would cause?
tensors
tensors
asked Dec 24 '18 at 5:17
Ion SmeIon Sme
11510
asked Dec 24 '18 at 5:17
Ion SmeIon Sme
11510
edited Dec 25 '18 at 5:08
Ion Sme
asked Dec 24 '18 at 5:17
Ion SmeIon Sme
11510
asked Dec 24 '18 at 5:17
Ion SmeIon Sme
11510
asked Dec 24 '18 at 5:17
Ion SmeIon Sme
11510
11510
add a comment |
add a comment |
1 Answer
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The reason for that not being allowed is that the result is not a tensor. It doesn't transform in a good way when the coordinate system is changed.
answered Dec 24 '18 at 10:20
md2perpemd2perpe
8,22111028
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$begingroup$
The reason for that not being allowed is that the result is not a tensor. It doesn't transform in a good way when the coordinate system is changed.
answered Dec 24 '18 at 10:20
md2perpemd2perpe
8,22111028
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add a comment |
$begingroup$
The reason for that not being allowed is that the result is not a tensor. It doesn't transform in a good way when the coordinate system is changed.
answered Dec 24 '18 at 10:20
md2perpemd2perpe
8,22111028
$endgroup$
add a comment |
$begingroup$
The reason for that not being allowed is that the result is not a tensor. It doesn't transform in a good way when the coordinate system is changed.
answered Dec 24 '18 at 10:20
md2perpemd2perpe
8,22111028
$endgroup$
The reason for that not being allowed is that the result is not a tensor. It doesn't transform in a good way when the coordinate system is changed.
answered Dec 24 '18 at 10:20
md2perpemd2perpe
8,22111028
answered Dec 24 '18 at 10:20
md2perpemd2perpe
8,22111028
answered Dec 24 '18 at 10:20
md2perpemd2perpe
8,22111028
answered Dec 24 '18 at 10:20
md2perpemd2perpe
8,22111028
8,22111028
add a comment |
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