1 files changed, 106 insertions, 0 deletions
diff --git a/260/CH5/EX5.12/5_12.sce b/260/CH5/EX5.12/5_12.sce
new file mode 100644
index 000000000..b519b3b41
--- /dev/null
+++ b/260/CH5/EX5.12/5_12.sce
@@ -0,0 +1,106 @@
+//Eg-5.12
+//pg-242
+
+clear
+clc
+
+A=[1 2 3;2 3 5;3 5 5];
+
+//Iteration Number----1
+
+//for i=1,j=2
+sigma=sum(diag(A).^2);
+S=sum(A.^2);
+q=abs(A(1,1)-A(2,2));
+p=2*A(1,2)*q/(A(1,1)-A(2,2));
+spq=(p^2+q^2)^.5;
+cosalp=((1+q/spq)/2)^.5;
+sinalp=p/(2*cosalp*spq);
+U=[cosalp sinalp 0;sinalp -cosalp 0;0 0 1];
+
+//for i=1,j=3
+A1=inv(U)*A*U;
+
+q=abs(A1(1,1)-A1(3,3));
+p=2*A1(1,3)*q/(A1(1,1)-A1(3,3));
+spq=(p^2+q^2)^.5;
+cosalp=((1+q/spq)/2)^.5;
+sinalp=p/(2*cosalp*spq);
+U1=[cosalp 0 sinalp;0 1 0;sinalp 0 -cosalp];
+
+
+//for i=2,j=3
+A2=inv(U1)*A1*U1;
+
+q=abs(A2(2,2)-A2(3,3));
+p=2*A2(2,3)*q/(A2(2,2)-A2(3,3));
+spq=(p^2+q^2)^.5;
+cosalp=((1+q/spq)/2)^.5;
+sinalp=p/(2*cosalp*spq);
+U2=[1 0 0 ;0 cosalp sinalp;0 sinalp -cosalp];
+
+A3=inv(U2)*A2*U2;
+
+sig2=sum(diag(A3.^2));
+T=U*U1*U2;
+
+//Iteration number ---2
+
+A=A3;
+//for i=1,j=2
+sigma=sum(diag(A).^2);
+S=sum(A.^2);
+q=abs(A(1,1)-A(2,2));
+p=2*A(1,2)*q/(A(1,1)-A(2,2));
+spq=(p^2+q^2)^.5;
+cosalp=((1+q/spq)/2)^.5;
+sinalp=p/(2*cosalp*spq);
+U=[cosalp sinalp 0;sinalp -cosalp 0;0 0 1];
+
+//for i=1,j=3
+A1=inv(U)*A*U;
+
+q=abs(A1(1,1)-A1(3,3));
+p=2*A1(1,3)*q/(A1(1,1)-A1(3,3));
+spq=(p^2+q^2)^.5;
+cosalp=((1+q/spq)/2)^.5;
+sinalp=p/(2*cosalp*spq);
+U1=[cosalp 0 sinalp;0 1 0;sinalp 0 -cosalp];
+
+
+//for i=2,j=3
+A2=inv(U1)*A1*U1;
+
+q=abs(A2(2,2)-A2(3,3));
+p=2*A2(2,3)*q/(A2(2,2)-A2(3,3));
+spq=(p^2+q^2)^.5;
+cosalp=((1+q/spq)/2)^.5;
+sinalp=p/(2*cosalp*spq);
+U2=[1 0 0 ;0 cosalp sinalp;0 sinalp -cosalp];
+
+A3=inv(U2)*A2*U2;
+T6=T*U*U1*U2;
+
+sig3=sum(diag(A3.^2));
+
+printf('The values of the sigmas are\n    sigma1 = %f\n    sigma2 = %f\n',sig2,sig3)
+T = A.^2;
+Sumofsqrs = sum(T);
+printf('\nThe sum of squares of the elements of the given original matrix = %f\n',Sumofsqrs)
+printf('\nSum of squares of all elements is equal to sigma2\n')
+printf('\nThe eigen values are as follows\n')
+disp(diag(A3))
+printf('\nThe corresponding eigen vectors are columns of the following matrix\n')
+disp(T6)
+for(i = 1:3)
+    eigenv(i) = A3(i,i);
+end
+
+printf('\n\nThe checklist given at the end of the problem \n')
+printf('\n1. The sum of eigen values = %f\n   The trace of the original matrix = %f\n',sum(eigenv),trace(A))
+printf('\n2. The product of eigenvalues = %f\n   The determinant of the original matrix = %f\n',eigenv(1)*eigenv(2)*eigenv(3),det(A))
+
+    dot(1) = sum(T6(:,1).*T6(:,2));
+    dot(2) = sum(T6(:,1).*T6(:,3));
+    dot(3) = sum(T6(:,3).*T6(:,2));
+printf('\n3. The dot product of eigen vectors 1&2 = %f\n   The dot product of eigen vectors 1&3 = %f\n   The dot product of eigen vectors 3&2 = %f\n=> The eigen vecotrs are orthonormal\n',dot(1),dot(2),dot(3))
+\ No newline at end of file