LaTeX Guidelines

This notation guide is inspired by Deep Learning by Ian Goodfellow, Yoshua Bengio and Aaron Courville whilst trying to stay short and compatible with KaTeX (Docusaurus support) and MathJax (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{\mathbf{A}} which is sadly not nice and short.

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

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

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

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}`	\(\Bbb{C}\)