linear algebra

A note on notation

$a,\alpha$ … scalars (single numbers); normal/italic font
$\mathbf{x}\in {\mathbb{R}}^{d\times 1}$ … vector, by default a column vector; bold font
$\mathbf{A}\in {\mathbb{R}}^{m\times n}$ … matrix, by default capital bold font
$\hat{\mathbf{u}}$ … arbitrary unit vector
${\mathbf{e}}_i$ … basis vector (1 at position $i$, 0 elsewhere)
TODO: move the below to where they actually fit better
$X,Y$ … random variables
$\mathbf{X},\mathbf{Y}$ … random vectors
$x\in X$ … realization of random variable $X$
$\mathbf{x}\in \mathbf{X}$ … realization of random vector $\mathbf{X}$
$\hat{\theta },\hat{y},\hat{f}$ … estimates or predictions
$\mathcal{X},\Omega ,\mathcal{D}$ … set / space

$f:A\to B$ … function $f$ mapping from set $A$ to set $B$
$f(a;b,c)$ … function $f$ with argument $a$ and parameters $b,c$