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//Eg-3.10
//pg-92
clear
clc
//cholesky decomposition
A=[2 1 0;1 2 1;0 1 2];
B=[3.6;6.7;-1.9];
if A==A' then
disp("A is symmetric and we have to check whether it is positive definite or not")
end
for k=1:3
s(k)=det(A(1:k,1:k));
end
j=min(s);
if j>0 then
disp("given matrix is positive definite and hence cholesky decomposition can be performed")
[n,n]=size(A);
summ1=0;
summ2=0;
for i=1:n
summ1=0;
for k=1:i-1
summ1=summ1+(L(i,k))^2;
end
L(i,i)=(A(i,i)-summ1)^(1/2);
for j=i+1:n
summ2=0;
for k=1:i-1
summ2=summ2+L(i,k)*L(j,k);
end
L(j,i)=(A(i,j)-summ2)/(L(i,i));
end
end
if L*L'==A then
disp("verification was done")
end
Y=inv(L)*B;
X=inv(L')*Y;
disp(X)
end
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