# Math Help - Trace of a Tensor

1. ## 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

2. ## Re: Trace of a Tensor

If, for example, x= ai+ bj+ ck, in some coordinate system then x tensor x is represented, in that same coordinate system by $\begin{bmatrix}a^2 & ab & ac \\ ab & b^2 & bc \\ ac & bc & c^2\end{bmatrix}$. Yes, the trace of that is $x\cdot x= a^2+ b^2+ c^2$.