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

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- Nov 14th 2012, 07:20 AMtoluunTrace 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 - Nov 14th 2012, 09:12 AMHallsofIvyRe: 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 $\displaystyle \begin{bmatrix}a^2 & ab & ac \\ ab & b^2 & bc \\ ac & bc & c^2\end{bmatrix}$. Yes, the trace of that is $\displaystyle x\cdot x= a^2+ b^2+ c^2$.