MATLAB: Using recursive method for finding the determinant of a matrix

determinantMATLAB

Hello, I'd like to find the determinant of a matrix without using built-in functions.
I thought of using cofactor expansion, and this is my code.
(I'm very new to this MATLAB programming, and I have very little knowledge about this part.)
I'm actually not sure if I could arrange the codes like that.
I could really use some help, please. Thank you for reading.
function det=myDet(A)
if size(A)==[2 2]
    a_ij=A(i, j);
    det=(a_11)*(a_22)-(a_12)*(a_21);
else
    i=1:n;
    A(:,1)=[];
    A(i,:)=[];
    A=A_i;
    det=symsum((((-1)^(i+1))*myDet(A_i)),i,1,n)
end
end

Best Answer

It looks like what you have in mind could be implemented like this:
function det = myDet(A)
if isequal(size(A),[2 2])
    det = A(1,1)*A(2,2)-A(1,2)*A(2,1);
else
    det = 0;
    top_row = A(1,:);
    A(1,:) = [];
    for i = 1:size(A,2)
        A_i = A;
        A_i(:,i) = [];
        det = det+(-1)^(i+1)*top_row(i)*myDet(A_i);
    end
end
end
But note that there is nothing special about the 2-by-2 case, so you could let the recursion go all the way down to the scalar case:
function det = myDet(A)
if isscalar(A)
    det = A;
    return
end
det = 0;
top_row = A(1,:);
A(1,:) = [];
for i = 1:size(A,2)
    A_i = A;
    A_i(:,i) = [];
    det = det+(-1)^(i+1)*top_row(i)*myDet(A_i);
end
end
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