Inverse / Division of Matrix using Adjoint Method

Inverse.m

clc;
clear all;
close all;

disp('Inverse of a matrix using Adjoint Method')
        disp('------------------------------------------------')
        prompt = 'Enter the order of the matrix ';
        m = input(prompt);
        % initializes the variable M
        M=zeros(m,m);
N=zeros(m,m);
        % Entering random values in matrices
        for i=1:m
            for j=1:m
                M(i,j)=random('unid',10);
            end
        end
d = detrminant(M,m);
        disp('The determinant is ');
disp(num2str(d,2));
if d==0
disp('Matrix is not inversible');
else
cofactors(d,M,m,N,2,m); % N,2,m for separating division operation from inverse operation
end


detrminant.m

function d=detrminant(M,m)

det=0;
s=1;
N=zeros(m,m);
if (m==1)
d=M(1,1); return
else
det = 0;
for c=1:m
p = 1;
q = 1;
for i=1:m
for j=1:m
if (i~=1 && j~=c)
N(p,q)=M(i,j);
if (q<(m-1))
q=q+1;
else
q=1;
p=p+1;
end
end
end
end
det=det+s*(M(1,c)*detrminant(N,m-1));
s=-1*s;
end
end
d=det; return

cofactors.m

function cofactors(det,M,m,Q,u,f)

N=zeros(m,m);
fac=zeros(m,m);
for q=1:m
for p=1:m
m1 = 1;
n1 = 1;
for i=1:m
for j=1:m
if (i~=q && j~=p)
N(m1,n1) = M(i,j);
if (n1 < (m - 1))
n1=n1+1;
else
n1 = 1;
m1=m1+1;
end
end
end
end
fac(q,p)=power(-1,q+p)*detrminant(N,m-1);
end
end

trans(det,M,fac,m,Q,u,f); % transpose of cofactor matrix i.e. adjoint matrix

trans.m

function trans(det,mat,fac,r,Q,u,f)

N=zeros(r,r);

inv=zeros(r,r);

for i=1:r

for j=1:r

N(i,j)=fac(j,i);

end

end

for i=1:r

for j=1:r

inv(i,j)=N(i,j) / det;

end

end

disp('=============================================');

disp('     THE INVERSE OF THE MATRIX');

disp('=============================================');

disp(inv);

nonsingular(mat,inv,r,Q,u,f);

nonsingular.m

function nonsingular(mat,inv,r,Q,u,f)

if (u==2)

count=0;

I=zeros(r,r);

for i=1:r

for j=1:r

sum=0;

for k=1:r

sum=sum+mat(i,k)*inv(k,j);

end

I(i,j)=sum;

end

end    

disp('=============================================');

disp('     CHECK FOR SINGULAR OR NON-SINGULARITY');

disp('=============================================');

disp(I);

for i=1:r

for j=1:r

if(i==j && int8(I(i,j))==1)

count=count+1;

end

end

end

if(count==r)

disp('Non-Singular/Invertible Inverse Matrix');

else

disp('Singular/Non-Invertible Inverse Matrix');

end

elseif (u==1)

DIV=zeros(f,r);

for i=1:f

for j=1:r

sum=0;

for k=1:r

sum=sum+Q(i,k)*inv(k,j);

end

DIV(i,j)=sum;

end

end    

disp('=============================================');

disp('     DIVISION OF TWO MATRICES');

disp('=============================================');

disp(DIV);

end