Notation

Functions are denoted by lowercase italic letters: $f$, $g$, $h$, $x$, $y$, $z$. Independent variables will be dropped when brevity demands it.

Lowercase letters with an arrow above — $\overrightarrow{v}$, $\overrightarrow{u}$, $\overrightarrow{x}$.

Short for "In Anticipation of Friendly Fire." I will leave out details when I feel like they aren't serving a useful purpose. I'm aware of the details, I just don't want to write them down.

Capital sans-serif letters — $𝖠$, $𝖬$, $𝖯$. Inverses and transposes inherit the convention: ${𝖬}^{-1}$, ${𝖯}^{\top }$.

In general, sets will be denoted by capital bold letters: $𝐀$. When referring to element of a set we use the corresponding lowercase letter e.g., $a\in 𝐀$.

Certain named sets will use blackboard bold:

• the natural numbers: $\mathbb{N}$,
• the integers: $\mathbb{Z}$,
• the rational numbers: $\mathbb{Q}$,
• the real numbers: $ℝ$,
• the complex numbers: $ℂ$.

Calligraphic capital letters for operators that act on functions or function spaces — Laplacians, integral kernels, differential operators. For example: $ℒ$, $𝒟$, $𝒯$. Read as "L-beautiful".

Capital script letters for function spaces — $\mathcal{H}$ for a Hilbert space, $\mathcal{C}$ for a class of smooth functions, etc.