The below code is to obtain eigen value with the help of Givens rotation method, where the matrix is converted into tridigonal form first and then its eigenvalues are obtained.
The code below works fine for some cases but doesn't give eigenvalues at certain cases.
Ex- A =[-6 2 1;2 -9 -4; 1 -4 -9];
The output is :
root(z^3 + 24*z^2 + 168*z + 361, z, 1)
root(z^3 + 24*z^2 + 168*z + 361, z, 2)
root(z^3 + 24*z^2 + 168*z + 361, z, 3)
Can anyone tell me what I have been missing?
Thankyou for your efforts in advance :)
function eigen_values = given(B)
syms x
[m,n] = size(B);
if nargin>1
fprintf('Please enter only one Matrix');
return;
end
if isscalar(B) || (m ~= n)
fprintf('Please enter a Square matrix \n');
return;
elseif m ==2
fprintf('Please enter a Square matrix grater than 2X2 \n');
return ;
elseif ~isreal(B)
fprintf('All elements of the input matrix should belong to real number domain except infinity and negative infinity \n');
return ;
elseif find((isfinite(B))==0)
fprintf('Please enter a matrix with finite number as its elements \n');
return;
end
S = eye(m);
j =2;
N = ((m-1)*(m-2))/2;
I = eye(m);
theta = atan(B(1,j+1)/B(1,2));
for i = 1:N
fprintf('Rotation %d : \n',i);
theta = atan(B(1,j+1)/B(1,2));
S(2,2) = cos(theta);
S(2,j+1) = -sin(theta);
S(j+1,2) = sin(theta);
S(j+1,j+1) = cos(theta);
S
B = S'*B*S
j =j+1;
S = eye(m);
if j >m
break;
end
end
eqn = det(B-x*I);
eigen_values = solve(eqn);
end
