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

• the imaginary number is generally referred to as $i$ in physics, its meaning should be implicit from the context.