# Notation

The HOOMD-blue documentation uses the following mathematical notation.

General notation:

\(x\) |
Scalar. |

\(\vec{a}\) |
Vector. |

\(a\) |
Magnitude of the vector \(\vec{a}\). |

\(\hat{a}\) |
Unit vector in the direction of \(\vec{a}\). |

\(\mathbf{A}\) |
Matrix. |

\(\mathbf{b}\) |
Quaternion. |

\(\vert \mathbf{b} \vert\) |
Magnitude of a quaternion. |

\(i\), \(j\), \(k\) |
Indices. |

\(i\) |
\(\sqrt{-1}\) in some contexts. |

\(\mathrm{function}\) |
A mathematical function. |

a \([\mathrm{length}]^2\) |
The quantity “a” has dimensions of \(\mathrm{length}^2\). |

Symbol definitions:

\(\vec{v}_{ij}\) |
\(\vec{v}_j - \vec{v}_j\) |

\(\vec{r}\) |
Position. |

\(\vec{v}\) |
Velocity. |

\(\mathbf{q}\) |
Orientation. |

\(m\) |
Mass. |

\(\vec{p}\) |
Momentum. |

\(I\) |
Moment of inertia. |

\(q\) |
Charge. |

\(N\) |
Number. |

\(L\) |
Length. |

\(V\) |
Volume. |

\(P\) |
Pressure. |

\(\rho\) |
Number density. |

\(\vec{a}_1\), \(\vec{a}_2\), \(\vec{a}_3\) |
Box unit cell vectors. |

\(\vec{F}\) |
Force. |

\(\vec{\tau}\) |
Torque. |

\(U\) |
Potential energy. |

\(K\) |
Kinetic energy. |

\(E\) |
Total energy. |

\(T\) |
Temperature. |

\(k\) |
Boltzmann’s constant in some contexts. Typically appears multiplying temperature: \(kT\). |

\(k\) |
Spring constant in some contexts. |

\(\beta\) |
\(\frac{1}{kT}\) |

\(t\) |
Time. |