🎬a type (2,0) tensor that is initially symmetric and the transformed tensor remains symmetric

A tensor's symmetry is a fundamental property that is preserved under coordinate transformations. The demo visually confirms that even as the tensor's individual components change and the coordinate system rotates, the relationship between the off-diagonal elements remains symmetrical, proving that if $T^{a b}=T^{b a}$, then $T^{\prime a^{\prime} b^{\prime}}=T^{\prime b^{\prime} a^{\prime}}$. This shows that symmetry is an intrinsic characteristic of the tensor itself, not just a feature of how it's represented in a particular coordinate system.

Proving Symmetry of a Rank-2 Tensor | Proof and Derivationviadean on Notion