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//Example 4.16
//Strum Sequence
//Page no. 117
clc;clear;close;
A=[8,-6,2;-6,7,-4;2,-4,3]
disp(A,'A=')
k=0;
for j=2:3
k=k+A(j,1)^2;
end
a=A(2,1)*abs(1/A(2,1))*sqrt(k);
U=[0;a+A(2,1);A(3,1)];
U1=U'*U;
U2=U*U';
P=eye(3,3)-(2*U2)/U1;
B=P*A*P;
disp(B,'Reduced Matrix = ');
lb=poly(0,"lb")
f0l=1; //strum sequence
f1l=(B(1,1)-lb)*f0l;
f2l=(B(2,2)-lb)*f1l-B(1,2)^2*f0l
f3l=(B(3,3)-lb)*f2l-B(2,3)^2*f1l
disp(f3l,"f3(lambda) = ")
disp(roots(f3l),"Therefore the eigenvalues are : ")
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