📢The Invariant Nature of Tensor Symmetry Under Coordinate Transformations

Tensor symmetry is an invariant property. The proof shows that if a tensor is symmetric in one coordinate system, it will always be symmetric in any other transformed coordinate system. This is demonstrated by applying the tensor transformation rule and using the initial symmetry to rearrange terms. The fact that the property holds true across all coordinate systems makes symmetry a fundamental characteristic of the tensor itself, rather than a coincidental feature of a specific coordinate representation.

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