Common Symbols

$P \implies Q$

$P$ implies $Q$

$P \iff Q$

$P \implies Q$ and $Q \implies P$

$a := 1$

$a$ is defined as equal to 1

$\RR$

all real numbers

$\NN$

the natural numbers $\{1, 2, \ldots \}$

$\range T$

range of function $T$

$\inner{\boldx, \boldy}$

inner product of $\boldx$ and $\boldy$

$\bolde_n$

$n$th canonical basis vector

$\|\boldx\|$

norm of $\boldx$

$\boldx \perp \boldy$

$\boldx$ and $\boldy$ are orthogonal

$S^{\perp}$

orthogonal complement of $S$

$\proj S$

orthogonal projection onto subspace $S$

$\boldI$

identity matrix

$\boldA^\T$

transpose of $\boldA$

$\diag(d_1, \ldots, d_N)$

diagonal matrix with diagonal elements $(d_1, \ldots, d_N)$

$\lL(x)$

distribution (or law) of random variable $x$

$\bB(\RR^N)$

Borel sets

$\bB$-measurable

Borel measurable

$\nN(\mu, \sigma^2)$

normal distribution with mean $\mu$ and variance $\sigma^2$

$\Phi$

standard normal CDF

$\phi$

standard normal density

$\1_B$

indicator function of set $B$

IID

independent and identically distributed

$\zdata$

data set

$\Zdata$

sample space