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

Math symbols

Basic

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

\(\mathbb{X}\): 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 \(\sigma^2\).

\( k \): Kernel function.
\(\boldsymbol{K}\): Gram matrix, defined as \(\boldsymbol{K}_{ij} = k(\boldsymbol{x}_i, \boldsymbol{x}_j)\).
\(\boldsymbol{K}_{ij}\): The element at row \( i \) and column \( j \) of \(\boldsymbol{K}\).