necessary and sufficient condition for diagonalizability

Let $k$ be a field, $V$ a vector space over $k$ of dimension $n$, and $T\in \mathrm{End}(V)$. 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
Canonical name	NecessaryAndSufficientConditionForDiagonalizability
Date of creation	2013-03-22 14:15:41
Last modified on	2013-03-22 14:15:41
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	11
Author	Mathprof (13753)
Entry type	Theorem
Classification	msc 15A04