# 15.1. List of Main Symbols¶

The main symbols used in this book are listed below.

## 15.1.1. Numbers¶

Symbol Type
$$x$$ Scalar
$$\mathbf{x}$$ Vector
$$\mathbf{X}$$ Matrix
$$\mathsf{X}$$ Tensor

## 15.1.2. Sets¶

Symbol Type
$$\mathcal{X}$$ Set
$$\mathbb{R}$$ Real numbers
$$\mathbb{R}^n$$ Vectors of real numbers in $$n$$ dimensions
$$\mathbb{R}^{a \times b}$$ Matrix of real numbers with $$a$$ rows and $$b$$ columns

## 15.1.3. Operators¶

Symbol Type
$$\mathbf{(\cdot)} ^\top$$ Vector or matrix transposition
$$\odot$$ Element-wise multiplication
$$\lvert\mathcal{X }\rvert$$ Cardinality (number of elements) of the set $$\mathcal{X}$$
$$\|\cdot\|_p$$ $$L_p$$ norm
$$\|\cdot\|$$ $$L_2$$ norm
$$\sum$$ Series addition
$$\prod$$ Series multiplication

## 15.1.4. Functions¶

Symbol Type
$$f(\cdot)$$ Function
$$\log(\cdot)$$ Natural logarithm
$$\exp(\cdot)$$ Exponential function

Symbol Type
$$\frac{dy}{dx}$$ Derivative of $$y$$ with respect to $$x$$
$$\partial_{x} {y}$$ Partial derivative of $$y$$ with respect to $$x$$
$$\nabla_{\mathbf{x}} y$$ Gradient of $$y$$ with respect to $$\mathbf{x}$$

## 15.1.6. Probability and Statistics¶

Symbol Type
$$\Pr(\cdot)$$ Probability distribution
$$z \sim \Pr$$ Random variable $$z$$ obeys the probability distribution $$\Pr$$
$$\Pr(x|y)$$ Conditional probability of $$x|y$$
$${\mathbf{E}}_{x} [f(x)]$$ Expectation of $$f$$ with respect to $$x$$

## 15.1.7. Complexity¶

Symbol Type
$$\mathcal{O}$$ Big O notation
$$\mathcal{o}$$ Little o notation (grows much more slowly than)