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.

,

where

is a second order tensor and

is the repeated suffix. Is

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

, where it is mentioned that

is a scalar. Why is

a zeroth order tensor, i.e. a scalar? I would not expect that since two different suffices are used.