LaTeX Guidelines

This notation guide is inspired by Deep Learning by Ian Goodfellow, Yoshua Bengio and Aaron Courville (opens in a new tab) whilst trying to stay short and compatible with KaTeX (opens in a new tab) (Docusaurus support) and MathJax (opens in a new tab) (Jupyter Notebook support). This page is also meant as a cheat sheet for me on latex structures such as matrices etc.

Numbers and Arrays

If we wanted tensors to also be bold we would have to write \mathsf{\boldsymbol{A}} which is sadly not nice and short.

Description	Code	Example
Scalar (integer or real)	`a=2`	$a$
Vector, lowercase italic bold	`\boldsymbol{a}`	$\boldsymbol{a}$
Matrix, uppercase italic bold	`\boldsymbol{A}`	$\boldsymbol{A}$
Tensor, uppercase sans-serif	`\mathsf{A}`	$\mathsf{A}$
Identity matrix with $n$ rows and $n$ columns	`\boldsymbol{I}_n`	$\boldsymbol{I}_n$
Identity matrix with implied dimensionality	`\boldsymbol{I}`	$\boldsymbol{I}$
Square diagonal matrix with elements along main diagonal given by $\boldsymbol{a}$	`\text{diag}(\boldsymbol{a})`	$\text{diag}(\boldsymbol{a})$

Description	Code	Example
Element $i$ of vector $\boldsymbol{a}$ , with indexing starting at 1	`a_i`	$a_i$
All elements of vector $\boldsymbol{a}$ except for element $i$	`a_{-i}`	$a_{-i}$
Element $i,j$ of matrix $\boldsymbol{A}$ , with $i$ corresponding to the row index and $j$ the column index	`A_{i,j}` or `a_{ij}`	$A_{i,j}$ or $a_{ij}$
Row $i$ of matrix $\boldsymbol{A}$	`\boldsymbol{A}_{i,:}`	$\boldsymbol{A}_{i , :}$
Column $j$ of matrix $\boldsymbol{A}$	`\boldsymbol{A}_{:,j}`	$\boldsymbol{A}_{: , j}$

Description	Code	Example
Tranpose of matrix $\boldsymbol{A}$	`\boldsymbol{A}^T`	$\boldsymbol{A}^T$
Moore-Penrose pseudoinverse of matrix $\boldsymbol{A}$	`\boldsymbol{A}^\dagger`	$\boldsymbol{A}^\dagger$
Hadamard (element-wise) product of $\boldsymbol{A}$ and $\boldsymbol{B}$	`\boldsymbol{A} \odot boldsymbol{B}`	$\boldsymbol{A} \odot \boldsymbol{B}$
Determinant of matrix $\boldsymbol{A}$	`\text{det}(\boldsymbol{A})`	$\text{det}(\boldsymbol{A})$
Trace of matrix $\boldsymbol{A}$	`\text{tr}(\boldsymbol{A})`	$\text{tr}(\boldsymbol{A})$

Description	Code	Example
Set	`A`	$A$
Set of natural numbers, including $0$	`\Bbb{N}=\{0,1,2,3,...\}`	$\Bbb{N}=\{0,1,2,3,...\}$
Set of integer numbers	`\Bbb{Z}`	$\Bbb{Z}$
Set of rational numbers	`\Bbb{Q}`	$\Bbb{Q}$
Set of irrational numbers	`\Bbb{I}`	$\Bbb{I}$
Set of real numbers	`\Bbb{R}`	$\Bbb{R}$
Set of complex numbers	`\Bbb{C}`	$\Bbb{C}$