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 $\displaystyle \begin{bmatrix}a^2 & ab & ac \\ ab & b^2 & bc \\ ac & bc & c^2\end{bmatrix}$. Yes, the trace of that is $\displaystyle x\cdot x= a^2+ b^2+ c^2$.