necessary and sufficient condition for diagonalizability

Let $k$ be a field, $V$ a vector space over $k$ of dimension $n$, and $T\in\operatorname{End}(V)$. Then $T$ is diagonalizable if and only if its minimal polynomial (http://planetmath.org/MinimalPolynomialEndomorphism) has no multiple roots and all its roots lie in $k$.

Title necessary and sufficient condition for diagonalizability NecessaryAndSufficientConditionForDiagonalizability 2013-03-22 14:15:41 2013-03-22 14:15:41 Mathprof (13753) Mathprof (13753) 11 Mathprof (13753) Theorem msc 15A04