Identify maximum difference in Matrix

Question

i am trying to find the Maximum difference between two matrices and identify where this maximum occurs.

I illustrate what I mean using an example. Given

X={{3, 1}, {8, 2}, {10, 3}}
Y={{5, 1}, {4, 2}, {5, 3}}

I calculate matrix which has (X-Y) and position as entries, specifically

d={{-2, 1}, {4, 2}, {5, 3}}

As out pout I would like to have

{5,3}

What is the best way to code this?

Answer 1

Depending on your taste,

d = MapThread[{#1[[1]] - #2[[1]], #1[[2]]} &, {X, Y}]

or

d = Transpose@{X[[All, 1]] - Y[[All, 1]], X[[All, 2]]}

define the differences d, if you need them. The symbol D is already in use in Mathematica, don't use it for variables.

Then you can compute

MaximalBy[d, Abs@*Last]

{{5, 3}}

As @HenrikSchumacher comments you don't really need the intermediate d though, and you don't need the second elements in each entry denoting their position: using Ordering is more elegant:

X = {3, 8, 10};
Y = {5, 4, 5};
j = First@Ordering[Abs[X - Y], -1]

3

(X - Y)[[j]]

5