Write down the form of general solution of EQ. x = Ax where A is a 3 × 3 real matrix for the following case, respectively:
• A has three different eigenvalues: λ1 > λ2 > λ3 ;
• A has a pair of complex conjugate eigenvalues: λ1,2 = a ± ib
• the characteristic polynomial of A, P (λ) = (λ − λ1 )^3 and one linear independent eigenvector v1 , dim(E) = 1.
• the characteristic polynomial of A, P (λ) = (λ − λ1 )^3 and two linear independent eigenvector v1 , dim(E) = 2.
Can anybody help me with this?
Thanks
• A has three different eigenvalues: λ1 > λ2 > λ3 ;
• A has a pair of complex conjugate eigenvalues: λ1,2 = a ± ib
• the characteristic polynomial of A, P (λ) = (λ − λ1 )^3 and one linear independent eigenvector v1 , dim(E) = 1.
• the characteristic polynomial of A, P (λ) = (λ − λ1 )^3 and two linear independent eigenvector v1 , dim(E) = 2.
Can anybody help me with this?
Thanks