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//Example 11.3
//Danilevsky Method
//Page no. 341
clc;close;clear;
A=[-1,0,0;1,-2,3;0,2,-3];
G=[A;eye(3,3)];
disp(G);
//transformation to frobenius matrix
for k=3:-1:2
g(k)=0;
for j=1:k-1
if(g(k)<G(k,j))
g(k)=G(k,j)
p=j;
end
end
if(g(k)~=0)
for j=1:3
r(1,j)=G(k,j)
end
for i=1:6
G(i,k-1)=G(i,k-1)/g(k)
end
disp(G)
for j=1:3
if(j~=k-1)
l=G(k,j)
for i=1:6
G(i,j)=G(i,j)-l*G(i,k-1)
end
end
end
disp(G)
end
for j=1:3
for i=1:3
c(i,1)=G(i,j)
end
G(k-1,j)=0
for i=1:3
G(k-1,j)=G(k-1,j)+r(1,i)*c(i,1)
end
end
disp(G)
end
//partition g
for i=4:6
for j=1:3
T(i-3,j)=G(i,j)
end
end
disp(T,'T=')
//eigenvalues computation
printf('\n\n\nCharateristic polynomial:')
p=poly(A,'x')
disp(p)
printf('\n\n\nEigenvalues:')
a=roots(p)
disp(a')
//eigenvectors computation
for k=1:3
m=2
for l=1:3
y(l,k)=a(k,1)^(m)
m=m-1;
end
end
printf('\n\n')
disp(y,'y=')
//eigenvector computation
for k=1:3
for l=1:3
y1(l,1)=y(l,1)
y2(l,1)=y(l,2)
y3(l,1)=y(l,3)
end
x1=T*y3;
x2=T*y2;
x3=T*y1;
end
printf('\n\nEigenvectors :\n')
for i=1:3
printf('|%.1f|\t\t|%.1f|\t\t|%.1f|',x1(i,1),x2(i,1),x3(i,1))
printf('\n')
end
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