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Matrix, eigenvalues and diagonalization

  • Thread starter jkeatin
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  • #1
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Matrix A= 1 2 0
2 1 0
2 -1 3



i got eigenvalues k=3 k=-1 what do i do after that to prove it is not able to be diagonalized
 

Answers and Replies

  • #3
tiny-tim
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i got eigenvalues k=3 k=-1 what do i do after that to prove it is not able to be diagonalized
Hi jkeatin! :smile:

-1 is a is a double eigenvalue …

so just plug -1 in and solve, and show that there is only one independent solution. :wink:
 
  • #4
HallsofIvy
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The point is that an n by n matrix is diagonalizable if and only if it has n independent eigenvectors. Since -1 is a double root of the characteristic polynomial, the matrix may not have two independent eigenvectors corresponding to eigenvalue -1. That is what you need to prove.
 
  • #5
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thanks guys, got it!
 

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