(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let M be a differentiable manifold, [itex]p \in M[/itex].

Suppose [itex] A \in T_{1,p}^1(M)[/itex] is symmetric with respect to its indices (i.e. [itex]A^i_j = A^j_i[/itex]) with respect to every basis.

Show that [itex] A^i_j = \lambda \delta^i_j[/itex], where [itex]\lambda \in \mathbb{R}[/itex].

2. Relevant equations

3. The attempt at a solution

I've tried various ways of using the change of basis formula to arrive at the desired result, but I can't make it work. I imagine I need to use something else that I'm not thinking of.

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# Homework Help: Linear Algebra/Tensor Algebra: Symmetry of a (1,1) tensor.

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