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**amrasa81** Hello,

I have some basic problems with tensors and Einstein summation notation. As I understand, if a suffix appears twice in a tensor then summation over repeated indices is assumed, i.e.

$\displaystyle S_{ii} = S_{11} + S_{22} + S_{33}$,

where $\displaystyle S$ is a second order tensor and $\displaystyle i$ is the repeated suffix. Is $\displaystyle S_{ii}$ indirectly a zeroth order tensor, i.e. a scalar?

Einstein summation convention also states that a suffix cannot appear more than twice in an expression. I came across an expression for fourth order tensor $\displaystyle T_{iijj}$, where it is mentioned that $\displaystyle T_{iijj}$ is a scalar. Why is $\displaystyle T_{iijj}$ a zeroth order tensor, i.e. a scalar? I would not expect that since two different suffices are used.