Why does Theorem 2 6 not show that every matrix is diagonalizable (see Example 2 2) Any m Atilde n matrix of rank k is matrix equivalent to the m Atilde n matrix that is all zeros except that the first k diagonal entries are ones 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

Question: Why does Theorem 2.6 not show that every matrix is diagonalizable (see Example 2.2)? Any m Ã n matrix of rank k is matrix equivalent

Why does Theorem 2.6 not show that every matrix is diagonalizable (see Example 2.2)?
Any m Ã— n matrix of rank k is matrix equivalent to the m Ã— n matrix that is all zeros except that the first k diagonal entries are ones.

1 0 0 0. 0 0 0 0 0 0 1 0.. 0 0 0.. 0 0

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