Eigenvalue Problems
                             Chia-Ping Chen
                   Department of Computer Science and Engineering
                          National Sun Yat-sen University
                              Linear Algebra
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    Outline
           Eigenvalues and eigenvectors
           Eigen-decomposition and diagonalization
           Difference equation
           Differential equation
           Complex matrices
           Similar matrices
           Change of basis
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                                Chen P  Eigenvalue Problems
      notation
           Ax=λx: eigenvalue equation of matrix A
           |A−λI|=0: characteristic equation
           λ: eigenvalue
            i
           {λ ,:::,λ }: spectrum (the set of eigenvalues)
              1      k
           s : eigenvector corresponding to λ
            i                                i
           E : eigenspace corresponding to eigenvalue λ
             λi                                          i
           c∗: complex conjugate of c
           AH: Hermitian of A
           A∼B: similar matrices
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                               Chen P  Eigenvalue Problems
        Eigenvalue Equations
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                                          Chen P    Eigenvalue Problems