🧄Verifying the Rank Two Zero Tensor

The first part demonstrates that the zero tensor acts as the additive identity for tensor addition, just like the number zero in regular arithmetic. The second part establishes that this property-having all zero components-is invariant under coordinate transformations. This means that if a tensor is the zero tensor in one coordinate system, it will be the zero tensor in all others. This is proven by the tensor transformation law, which shows that multiplying the zero components by the rotation matrix results in zero components in the new coordinate system, confirming the zero tensor is a true tensor.

Verifying the Rank Two Zero Tensor | Proof and Derivationviadean on Notion