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