defective eigenvalues (repeated, complex and include zeros)

Hydroman S — Mon, 20 Apr 2009 04:15:03 -0400

The eigenvalues for the 6X6 (mass, damping, and stiffness) system described by the equation below include values which are: repeated, complex and include zeros
  m*y''(t)+c*y'(t)+k*y(t)=0

lam =

         0
         0
         0
   -0.0023
   -0.0023
   -0.0023
   -0.1421 - 0.7205i
   -0.1421 + 0.7205i
   -0.1421 - 0.7206i
   -0.1421 + 0.7206i
   -0.0846 - 0.8360i
   -0.0846 + 0.8360i

What would be the best way to handle the matrix A in Matlab in order to calculate the correct natral periods (eigenvalues) of the system.

n=6;
A=[zeros(n,n), eye(n,n); -m\[k, c]];
[U,lam]=eig(A); [lam,j]=sort(diag(lam)); U=U(:,j);

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defective eigenvalues (repeated, complex and include zeros)