List of Main Symbols¶

The main symbols used in this book are listed below.

Numbers¶

\(\mathcal{X}\)	Set
\(\mathbb{R}\)	Real number set
\(\mathbb{R}^n\)	Real number vector set of \(n\) dimension
\(\mathbb{R}^{x \times y}\)	Real number matrix set with \(x\) rows and \(y\) columns

\(\boldsymbol{(\cdot)}^\top\)	Vector or matrix transposition
\(\odot\)	Multiply by element
\(\lvert\mathcal{X}\rvert\)	Number of elements in the set \(\mathcal{X}\)
\(\\|\cdot\\|_p\)	\(L_p\) norm
\(\\|\cdot\\|\)	\(L_2\) norm
\(\sum\)	Continuous addition
\(\prod\)	Continuous multiplication

\(f(\cdot)\)	Function
\(\log(\cdot)\)	Natural logarithmic function
\(\exp(\cdot)\)	Exponential function

\(\frac{dy}{dx}\)	Derivative of \(y\) with respect to \(x\)
:math:`frac{partial y}{partial x}`	Partial derivative of \(y\) with respect to \(x\)
\(\nabla_{\cdot} y\)	Gradient of \(y\) with respect to \(\cdot\)

\(\mathbb{P}(\cdot)\)	Probability distribution
\(\cdot \sim \mathbb{P}\)	Random variable \(\cdot\) obeys the probability distribution \(\mathbb{P}\)
\(\mathbb{P}(\cdot \mid\cdot )\)	Conditional probability
\(\mathbb{E}_{\cdot}\left(f( \cdot)\right)\)	Expectation of \(f(\cdot)\) with respect to \(\cdot\)

\(\mathcal{O}\)

Big O notation