Matrix, eigenvalues and diagonalization

[jkeatin]

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

 

[NoMoreExams]

http://en.wikipedia.org/wiki/Diagonalizable_matrix#Matrices_that_are_not_diagonalizable ?

 

[tiny-tim]

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

Hi jkeatin!

-1 is a is a double eigenvalue …

so just plug -1 in and solve, and show that there is only one independent solution.

 

[HallsofIvy]

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.

 

[jkeatin]

thanks guys, got it!