# 14.1. List of Main Symbols¶

The main symbols used in this book are listed below.

## 14.1.1. Numbers¶

 $$x$$ Scalar $$\boldsymbol{x}$$ Vector $$\boldsymbol{X}$$ Matrix $$\mathsf{X}$$ Tensor

## 14.1.2. Sets¶

 $$\mathcal{X}$$ 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

## 14.1.3. Operators¶

 $$\boldsymbol{(\cdot)}^\top$$ 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

## 14.1.4. Functions¶

 $$f(\cdot)$$ 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