Matrices are not inherently rank-2 tensors. Matrices are just the formatting structure. The tensor described by the matrix must follow the transformation rules to be a tensor
- Components change according to mathematical formulae
## Dimension
- Dimensionality to the rank = number of components
An $n$-[rank](https://mathworld.wolfram.com/TensorRank.html) tensor in $m$-dimensional space is a mathematical object that has $n$ indices and $m^n$ components and obeys certain transformation rules
From <[wolfram](https://mathworld.wolfram.com/Tensor.html)>
