Suppose a matrix can be row reduced to the identity matrix, is this enough to say that it is not diagonalizable? If so, what theorem(s) or logic figures this out?
2026-04-02 03:20:56.1775100056
Is it possible to determine if a matrix is not diagonalizable via row operations?
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The matrices $\begin{pmatrix}1&1\\0&1\end{pmatrix}$ and $\begin{pmatrix}1&0\\0&1\end{pmatrix}$ can be obtained from one another by a row operation, yet one is diagonal and the other not diagonalizable.
Note that row operations "destroy" the identification between domain and target, which is essential to the notion of diagonalizabilty.