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.