# Define new operations for a matrix

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Radu Mihail on 28 Dec 2020
Commented: Radu Mihail on 29 Dec 2020
I have 2 vectors x=[0 1 2 0 1 0 3 1 0] and its transposed column vector y=x'
I need to define a new operation , let's say * following the multiplication table underneath
0 1 2 3
1 0 3 2
2 3 0 1
3 2 1 0
For instance under this new * commutative operation
0*1=1*0=1
1*1=0 or
3*2=1 or 2*3=1 or
3*3=0
And I would like to build a matrix A having first row x and first column y where the elements of the matrix would be each the result of individual element x.*y or y.*x but using only vectors x and y and defining the new operation * .
The result should be
A=[0 1 2 0 1 0 3 1 0; 1 0 3 1 0 1 2 0 1; 2 3 0 2 3 2 1 3 2; 0 1 2 0 1 0 3 1 0;1 0 3 1 0 1 2 0 1;0 1 2 0 1 0 3 1 0; 3 2 1 3 2 3 0 2 3;1 0 3 1 0 1 2 0 1;0 1 2 0 1 0 3 1 0]
A =
0 1 2 0 1 0 3 1 0
1 0 3 1 0 1 2 0 1
2 3 0 2 3 2 1 3 2
0 1 2 0 1 0 3 1 0
1 0 3 1 0 1 2 0 1
0 1 2 0 1 0 3 1 0
3 2 1 3 2 3 0 2 3
1 0 3 1 0 1 2 0 1
0 1 2 0 1 0 3 1 0

Stephen23 on 29 Dec 2020
Edited: Stephen23 on 29 Dec 2020
x = [0,1,2,0,1,0,3,1,0];
y = x.';
V = 0:3; % define value range of multiplication table
M = [0,1,2,3;1,0,3,2;2,3,0,1;3,2,1,0] % define multiplication table
M = 4×4
0 1 2 3 1 0 3 2 2 3 0 1 3 2 1 0
A = interp2(V,V,M,x,y)
A = 9×9
0 1 2 0 1 0 3 1 0 1 0 3 1 0 1 2 0 1 2 3 0 2 3 2 1 3 2 0 1 2 0 1 0 3 1 0 1 0 3 1 0 1 2 0 1 0 1 2 0 1 0 3 1 0 3 2 1 3 2 3 0 2 3 1 0 3 1 0 1 2 0 1 0 1 2 0 1 0 3 1 0
Radu Mihail on 29 Dec 2020
Thank you Stephen. This is simple and works perfectly

Steven Lord on 29 Dec 2020
You cannot define new operators for the double class, and I would strongly advise you not to try redefining multiplication for double.
You could define your own class and overload operators for that class. Or you could write a function that accepts two double inputs and call it instead of trying to use an operator.
Radu Mihail on 29 Dec 2020
I do not know how to write such a function.Would you kindly at least show me a type of function with double inputs to transform the vectors

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