How Do You Write the Diagonalized Moment of Inertia Tensor in Einstein Notation?

[frogjg2003]

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

 

[tiny-tim]

hi frogjg2003!

Is there a way to write this out, or am I stuck writing I_ij and having to remember that I_ii=I_i and I_i≠j=0?

you're stuck!

in practice, it doesn't matter

since either you only want one I_ii, 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