# Mathematical notation convention

In sisl we strive to make the documentation as consistent as possible. This should make reading different parts of the documentation simple to understand.

Here is a list of rules that sisl will strive to adhere to. If you find any inconsistencies in the documentation, please let us know!

• upper case characters such as $$I$$ and $$J$$ refer to atomic indices

• lower case characters such as $$i$$ and $$j$$ refer to orbital indices, e.g. $$i\in I$$

• scalars are represented via lower case italics, such as $$a$$

• vectors are represented via lower case bold faced, such as $$\mathbf a$$

One may use $$\hat{\mathbf a}$$ to signal normal vectors

• dot-products between vectors should be explicit $$\mathbf a\cdot\mathbf b$$

• matrices are represented via upper case bold faced, such as $$\mathbf A$$

• vector-matrix products are implicit $$\mathbf a\mathbf B$$

• matrix-matrix products are implicit $$\mathbf A\mathbf B$$

• Greek letters are used for other indices, such as spin ($$\sigma$$), Cartesian or lattice vectors.

• range of indices are denoted with $$\{ \}$$, such that, $$\{i\}$$ is an orbital index range, $$\{I\}$$ is an atomic index range and $$\{\alpha\}$$ refers to some other range which should be inferred from the context