The trace of tensor is defined as the sum of the diagonal elements;

Show, by performing a similarity transformation, that the trace is and invariant quantity, in other words, show that tr {l} = tr {1€™} where {l} is the tensor in one coordinate system and {l€™} is the tensor in a coordinate system rotated with respect to the first system. Verify this result for the different forms of the inertia tensor for a cube given in several examples in the text.

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tr{I} = 2 T