multiplicity of eigenvalue

Suppose V is a finite dimensional vector spaceMathworldPlanetmath over a field 𝔽, and suppose L:VV is a linear map. Suppose also that λ𝔽 is an eigenvalueMathworldPlanetmathPlanetmathPlanetmathPlanetmath of L, that is, det(L-λI)=0.

The algebraic multiplicity, denoted by Aλ(L), of λ is the multiplicity of the root λ to the polynomial det(L-λI)=0. The geometric multiplicity of λ, denoted by Gλ(L), is the dimensionPlanetmathPlanetmath of ker(L-λI), the eigenspaceMathworldPlanetmath of λ.

Title multiplicity of eigenvalue
Canonical name MultiplicityOfEigenvalue
Date of creation 2013-03-22 15:15:15
Last modified on 2013-03-22 15:15:15
Owner matte (1858)
Last modified by matte (1858)
Numerical id 5
Author matte (1858)
Entry type Definition
Classification msc 15A18
Defines geometric multiplicity
Defines algebraic multiplicity