This document describes the legend all the symbols used in the documentation of the project.

Math symbols

Basic

• \(x, y\): A scalar value.
• \(x, y, \dots\): A vector.
• \(A, B, \dots\): A matrix.
• \(A_{ij}\): The element at row \( i \) and column \( j \) of \( A \).
• \(A_{i:}\): The \( i \)-th row of \( A \).
• \(A_{:j}\): The \( j \)-th column of \( A \).
• \(A^T\): The transpose of \( A \).
• \(A^{-1}\): The inverse of \( A \).

Probability

• \(\mathbb{X}\): Polish sample space.
• \(\mathcal{B}(\mathbb{X})\): Borel \(\sigma\)-algebra on \(\mathbb{X}\).
• \(\mathbb{P}\): Probability measure.
• \(X, Y\): A random variable.
• \(\mathbb{R}\): The set of real numbers.
• \(\mathbb{R}^n\): The set of \( n \)-dimensional real vectors.
• \(\mathbb{R}^{m \times n}\): The set of \(m \times n\) real matrices.
• \(\mathbb{E}[X]\): The expected value of random variable \( X \).
• \(\mathcal{N}(\mu, \sigma^2)\): Normal distribution with mean \(\mu\) and variance \(\sigma^2\).

Control

• \(B: \mathbb{X} \times \mathbb{U} \to \mathbb{R}\): Barrier function.

Specific symbols

• \( k \): Kernel function.
• \( K \): Gram matrix, defined as \(K_{ij} = k(x_i, x_j)\).
• \(K_{ij}\): The element at row \( i \) and column \( j \) of \( K \).