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examples: eigenvalues, eigenvectors and diagonability

examples: eigenvalues, eigenvectors and diagonability. Pamela Leutwyler. Find the eigenvalues and eigenvectors. next. next. next. next. next. next. next. next. characteristic polynomial. next. characteristic polynomial. next. potential rational roots:1,-1,3,-3,9,-9.

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examples: eigenvalues, eigenvectors and diagonability

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  1. examples: eigenvalues, eigenvectors and diagonability Pamela Leutwyler

  2. Find the eigenvalues and eigenvectors next

  3. next

  4. next

  5. next

  6. next

  7. next

  8. next

  9. next

  10. characteristic polynomial next

  11. characteristic polynomial next

  12. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  13. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  14. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  15. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  16. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  17. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  18. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  19. potential rational roots:1,-1,3,-3,9,-9 synthetic division: This is not zero. 1 is not a root. next

  20. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  21. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  22. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  23. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  24. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  25. potential rational roots:1,-1,3,-3,9,-9 synthetic division: This is zero. -3 is a root. next

  26. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  27. potential rational roots:1,-1,3,-3,9,-9 synthetic division: next

  28. The eigenvalues are: -3, -3, -1 synthetic division: next

  29. The eigenvalues are: -3, -3, -1 To find an eigenvector belonging to the repeated root –3, consider the null space of the matrix –3I - A next

  30. The eigenvalues are: -3, -3, -1 To find an eigenvector belonging to the repeated root –3, consider the null space of the matrix –3I - A The 2 dimensional null space of this matrix has basis = next

  31. The eigenvalues are: -3, -3, -1 To find an eigenvector belonging to the repeated root –1, consider the null space of the matrix –1I - A The null space of this matrix has basis = next

  32. The eigenvalues are: -3, -3, -1 The eigenvectors are: next

  33. The eigenvalues are: -3, -3, -1 The eigenvectors are: next

  34. The eigenvalues are: -3, -3, -1 The eigenvectors are: A P –1 P diagonal matrix that is similar to A

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