The Minkowski distance of order p between two points
$${\displaystyle X=(x_{1},x_{2},\ldots ,x_{n}){\text{ and }}Y=(y_{1},y_{2},\ldots ,y_{n})\in \mathbb {R} ^{n}}$$
is defined as:
$${\displaystyle D\left(X,Y\right)=\left(\sum _{i=1}^{n}|x_{i}-y_{i}|^{p}\right)^{1/p}}$$
For a real number p ≥ 1, the p-norm or $L^p$-norm of x is defined by
$${\displaystyle \left\|x\right\|_{p}=\left(|x_{1}|^{p}+|x_{2}|^{p}+\dotsb +|x_{n}|^{p}\right)^{1/p}.}$$
it seems that the Minkowski distance is the $L^p$ norm of the distance between two points.
is my understanding right?