I have the proof that it works for diagonalizable matrices But does it work for the other category also? If it does or does not, how do I prove it?
Does the power iteration method for finding eigenvalues work for non diagonalizable matrices? Why or why not?
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linear-algebra
matrices
eigenvalues-eigenvectors
matrix-calculus
1 Answers
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Try power iteration with $$ \pmatrix{0 & 1 \\ 0 & 0 }, \ \pmatrix{0 & 1\\1& 0}, \ \pmatrix{0 & 1\\-1& 0}. $$
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0Only the first matrix you wrote is non-diagonalizable. However the problem with all of them is that they have 2 eigenvalues of the same "size". It has nothing to do with the diagonalizability of the matrix. – 2018-10-19