Notation#
Conventions used throughout the book include:
Boldface is used to denote vectors and matrices, the former in lowercase and the latter in uppercase. So \(\mathbf{X}\) is a matrix and \(\mathbf{x}\) is a (column) vector.
\(x\), \(y\), and \(z\) are generally variables, while \(f\) and \(g\) are functions. \(X\) is typically a random variable. Other Latin and Greek letters are usually parameters or constants.
Additional symbols include:
Symbol |
Meaning |
|---|---|
\(:=\) |
Is defined as |
\(\{1, 2, \ldots, n \}\) |
The set of integers from 1 to \(n\). In general \(\{\cdots\}\) denotes a set. |
\(x\in\mathcal{X}\) |
\(x\) is a member of the set \(\mathcal{X}\) |
\(\displaystyle \sum_{i=1}^n x_i\) |
Sum of \(x_1 + \ldots + x_n\). Also written as \(\sum_{i=1}^n x_i\). Alternatively, can write the summation of all elements in a set \(\mathcal{X}\) as \(\displaystyle \sum_{x\in \mathcal{X}} x\) or \(\sum_{x\in \mathcal{X}} x\) |
\(\R\) |
The real numbers |
\(\R^+\) |
The positive real numbers, \(\{x\in \R: x>0\}\) |
\(\forall i\) |
For all \(i\) |
\(\mathbf{x}'\) |
The transpose of \(\mathbf{x}\). Also applies to matrices. |
\(f(x) : \R \rightarrow [0,1]\) |
The function \(f\) maps from the real numbers to the closed interval 0 to 1 |
\(f'(x)\) or \(\frac{df}{dx}\) |
The derivative of \(f\) with respect to \(x\) |
\(\P\) |
Probability measure. Maps from the space of outcomes \(\Omega\) to a probability in \([0,1]\) |
\(\E(X)\) |
Expectation of random variable \(X\) |
\(\N(\mu,\sigma^2)\) |
Normal distribution with mean \(\mu\) and variance \(\sigma^2\) |