the eigenvaluas and the eigenvctors of the complex matrix?
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As we know, the eigenvctors of the complex matrix has the property of the orthogonality,but in fact, the results from the matlab obey the conlusion? why? the code is list as following:
mass matrix,stiffness matrix, and damping matrix
M = [1 0; 0 1];
C = [0.7 -0.1; -0.1 0.2];
K = [20000 -1; -1 20000];
f = [1 0];
%%system matrix
A = [C M; M zeros(2)];
B = [K zeros(2); zeros(2) -M];
F =[1 0 0 0]';
%%check the orthogonality
As = -inv(A)*B;
Bs = inv(A)*F;
Cs = [1, 0, 0, 0];
Ds = 0;
sys = ss(As,Bs,Cs,Ds);
t = 0:0.001:1;
impulse(sys,t);
[v,d] = eig(As,eye(4));
[m,n] = size(v);
vr = v(:,1:2:n);
vrr = v(:,2:2:n);
v = [vr vrr];
A = v'*v;
B = v'*As*v
A = inv(A)*A;
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