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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