Einstein notation question

  • Thread starter frogjg2003
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While taking notes in class, I was trying to write the moment of inertia tensor in Einstein notation as Iij instead of a 3x3 matrix, but when we diagonalized the matrix with diagonal elements Ii, I was confused on how to write it. Ii doesn't work because that means that treats it as a vector, instead of a matrix. Iiδij doesn't work for the same reason. Iiδjk doesn't work either because now it's a 3x3x3 tensor. Is there a way to write this out, or am I stuck writing Iij and having to remember that Iii=Ii and Ii≠j=0?
 

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  • #2
tiny-tim
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hi frogjg2003! :smile:
Is there a way to write this out, or am I stuck writing Iij and having to remember that Iii=Ii and Ii≠j=0?
you're stuck! :biggrin:

in practice, it doesn't matter

since either you only want one Iii, eg I11 (where there's no summation under the einstein convention anyway, because it only applies to dummy indices)

or you want the whole matrix
 

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