1. NUU Department of Electrical Engineering Linear Algedra ---Meiling CHEN1 Eigenvalues & eigenvectors Distinct eigenvalues Repeated eigenvalues –Independent eigenvectors –Generalize eigenvectors

2. NUU Department of Electrical Engineering Linear Algedra ---Meiling CHEN2 V is the basis of Null-space of (A-λI) Since (A-λI) have to a singular matrix If n-r=1 than we have one basis for null space  one eigenvector for one eigenvalue If n-r>1 means we have more than one vectors  More than one eigenvectors for one eigenvalue

3. NUU Department of Electrical Engineering Linear Algedra ---Meiling CHEN3 Case 1: depend V 1 and V 2 are Null-space of (A-λI)

4. NUU Department of Electrical Engineering Linear Algedra ---Meiling CHEN4 Case 2: depend

5. NUU Department of Electrical Engineering Linear Algedra ---Meiling CHEN5

6. NUU Department of Electrical Engineering Linear Algedra ---Meiling CHEN6 Case 3:Jordan form Generalized eigenvectors

7. NUU Department of Electrical Engineering Linear Algedra ---Meiling CHEN7 Example: