| 1. | This representation is useful in the diagonalization method for proofs.
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| 2. | However, I am concerned about the numerical stability in the diagonalization.
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| 3. | To prove the diagonalization theorem, take in.
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| 4. | This is the necessary and sufficient condition for diagonalizability and the canonical approach of diagonalization.
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| 5. | They are obtained by individual matrix diagonalization for each " J " value.
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| 6. | The matrix J is as close as one can come to a diagonalization of A.
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| 7. | However, we cannot do this for the real numbers-see Cantor's diagonalization argument.
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| 8. | The formal machinery of this proof is wholly elementary except for the diagonalization that the diagonal lemma requires.
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| 9. | One can complete the diagonalization of " T " by selecting an orthonormal basis of the kernel.
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| 10. | Given the diagonalizations of the submatrices, calculated above, how do we find the diagonalization of the original matrix?
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