---
tags:
  - maths
---
## Rank
-   Number of indices
-   Basis vectors per dimension/component
-   0
	-   Scalar
-   1
	-   Column Vector
-   2
	-   Square Matrix
-   3
	-   Cube matrix

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
![tensor](../img/tensor.png)
# Transformation Rules

1. Transforms like a tensor
2. Invariant to a change in coordinate system
	- 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)>