Trace of a Tensor

I am not sure which category this goes in but I thought this fit best.

I have a tensor x tensor x (when x is a vector)

What would be the trace of this tensor?

So tr(x tensor x)

I thought it would be x ∙ x.

Thanks

If, for example, x= ai+ bj+ ck, in some coordinate system then x tensor x is represented, in that same coordinate system by . Yes, the trace of that is .