# Relation between two vectors elements

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Lama Hamadeh on 30 Mar 2022
Commented: Torsten on 30 Mar 2022
Hi all,
suppose I have two vectors:
A = [1 2 3 4 5 6 7 8 9 10];
B = [4 7 8 2 1 10 3 5 9 6];
Ho can I say, the first element in B is the fourth element in A? In other workds, look at each element in B, what is its position/order/index in A? How can I establish a connection between both vectors' elements?
Thanks.

Torsten on 30 Mar 2022
Determine the permutation matrix P for which P*A = B:
A = [1 2 3 4 5 6 7 8 9 10].';
B = [4 7 8 2 1 10 3 5 9 6].';
P = bsxfun(@eq, A', B);
isequal(P * A, B)
Torsten on 30 Mar 2022
This code checks whether there are permutation matrices PL and PR such that
PL*A*PR = B,
i.e. whether there are permutations of the rows and columns of A such that you can arrive at B.
A = [1 2; 3 1; 4 1; 5 2];
B = [4 1; 5 2; 1 2; 3 1];
I1 = eye(size(A,1));
[~,a1] = sortrows(sort(A,2));
[~,b1] = sortrows(sort(B,2));
I2 = eye(size(A,2));
[~,a2] = sortrows(sort(A,1).');
[~,b2] = sortrows(sort(B,1).');
PL = I1(a1(b1),:)
PR = I2(:,a2(b2))
isequal(PL*A*PR,B)

### More Answers (1)

Geoff Hayes on 30 Mar 2022
@Lama Hamadeh - consider using intersect and in particular this example.