Minkowski Distance Function

$d(i,j)\ge 0$ if $i\ne j$ $d(i,j)=0$ if $i=j$ $d(i,j)=d(j,i)$ (Symmetrical) $d(i,j)\le d(i,k)+d(k,j)$ (Triangle inequality, going directly from object $i$ to object $j$ in space is no more than making a detour over any other object $k$)

$p$ = 1 : ($L_1$ norm) Manhattan distance $p$ = 2 : ($L_2$ norm) Euclidean distance $p$ $\to \infty$ : ($L_{\text{max}}$ norm, $L_{\infty }$ norm) Supremum distance Maximum distance between two objects