Mathematics

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Mathematical Syntax

Below is the mathematical typography that is used on this site.

A non-bold standard letter is used to denote a basic scalar:

$$ c = 3e8 $$

Bold font and an arrow is used to denote a vector:

$$ \b{\vec{v}} = \begin{bmatrix}1\\2\\3\end{bmatrix} $$

Bold font and a hat is used to denote a unit vector:

$$ \b{\hat{x}} = \begin{bmatrix}1\\0\\0\end{bmatrix} $$

A bold capital letter is used to denote a matrix or tensor:

$$ \b{B} = \begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix} $$

A bold lower-case letter is used to denote imaginary component(s) (in things such as complex numbers and quaternions).

$$ c = a + b\mathbf{i} $$

$$ q = a + b\mathbf{i} + c\mathbf{j} + d\mathbf{k} $$

A bar is used to indicate a conjugate:

$$ \bar{x} $$

The “triangle equals” is used to denote “is defined by”:

$$ F \triangleq ma $$

The Fourier Transform is denoted with \(\mathcal{F}\).

Belongs to uses the \in symbol from Latex (e.g. \(x\) belongs to the set of real numbers):

$$ x \in \mathbb{R} $$