necessary and sufficient condition for diagonalizability


Let k be a field, V a vector spaceMathworldPlanetmath over k of dimensionPlanetmathPlanetmathPlanetmath n, and TEnd(V). Then T is diagonalizablePlanetmathPlanetmath if and only if its minimal polynomialPlanetmathPlanetmath (http://planetmath.org/MinimalPolynomialEndomorphism) has no multiple rootsMathworldPlanetmath 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