MATLAB write a function that generates n x n matrix WITHOUT built in functions.

This problem requires me to use nested for loops to create matrix S of any given size. I took this to mean that the input would be an integer and output would be a matrix that is S=S^(-1) (invesre matrix) and that S*S=I (identity matrix). I'm a MATLAB beginner but so far I have this.

n=input("enter value of n: ");
S=zeros(n,n);
for i = 1:n
    for j = 1:n
        S(i,j)=i*j; % This is the part of the code I don't know how to fix.
    end   
end
S %prints matrix S
B = A' + A; 
B(1:n+1:end)=diag(A); %This part is supposed to take any square matrix and turn it symmetrical, it wont be nessesary if I can accomplish this is the first part of code.
C=inv(B);
C %should equal Identity matrix to check if my code worked correctly.

This code spits out a matrix but i cannot seem to find a way to (1) get it to give me a symmetrical matrix or (2) generate a matrix that I can then transform into a symmetrical matrix. If it helps at all the end goal is to have a matrix I can use as a DST (discrete sine transform) Any help would be appreciated thx.

Answer 1

[Walter Roberson]

Your S is symmetric.

However, your code uses the undefined variable A

B = A' + A; 
B(1:n+1:end)=diag(A); %This part is supposed to take any square matrix and turn it symmetrical, it wont be nessesary if I can accomplish this is the first part of code.

Typically the code would instead be

B = (A' + A)/2;

which has the advantage of leaving the values the same if the matrix was already symmetric. For example if A was ones(3,3) then your existing code would first create

B = 
   2 2 2
   2 2 2
   2 2 2

and then you would replace the diagonal to get

 B =
    1 2 2
    2 1 2
    2 2 1
    

which is a valid symmetric matrix, but the non-diagonal entries are now twice what they used to be.