Discussion for -Matrices and It’s Application

Procedure 1

A=input(“please input a matrix”)

M1=[];M2=[];M6=[];F=[];B=[];

n=size(A,1);RA=zeros(n,1);CA=zeros(n,1);

for k=1:n

    A=abs(A);

    RA(k)=[sum(A(k,:))-A(k,k)];

    CA(k)=[sum(A(:,k))-A(k,k)];

end

for i=1:n-1

    for j=i+1:n

    RR=RA(i)*RA(j);

    aa=abs(A(i,i)*A(j,j));

    CC=CA(i)*CA(j);

    if RR<aa&aa<CC

     M1=[M1;i,j];

     alpha=aa/RR;beta=CC/aa;gamma=alpha*beta;

     F=[F,alpha,beta,gamma];

    elseif CC<aa&aa<RR

     M2=[M2;i,j];

     x=aa/CC;y=RR/aa;z=x*y;

     B=[B,x,y,z];

    elseif RR>=aa&CC>=aa

     M6=1;break;

     Show=“the criterion is invalid”;

     end

    end

end

if M6==1

    “the criterion is invalid”;

    elseif size(M1,1)==0|size(M2,1)==0

     “A is an H-matrix”

     else

      k1=size(F,1);k2=size(B,1);

      for i=1:k1

      F2(i)=log(F(i,2))/log(F(i,3));

      end

      for i=1:k2

      B2(i)=log(B(i,2))/log(B(i,3));

      end

      if max(B2)+max(F2)<1

       show=“A is an H-matrix”

     end

end