Define new operations for a matrix

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

Answer 1

[Stephen23]

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]

Thank you Stephen. This is simple and works perfectly

Answer 2

[Steven Lord]

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]

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