multiplicity of eigenvalue

Suppose $V$ is a finite dimensional vector space over a field $\\mathbbmss{F}$ ,and suppose $L\\colon V\\to V$ is a linear map.Suppose also that $\\lambda\\in\\mathbbmss{F}$ is aneigenvalue of $L$ , that is, $\\operatorname{det}(L-\\lambda I)=0$ .

The algebraic multiplicity,denoted by $A_{\\lambda}(L)$ , of $\\lambda$ is the multiplicity of the root $\\lambda$ to the polynomial $\\operatorname{det}(L-\\lambda I)=0$ .The geometric multiplicity of $\\lambda$ , denoted by $G_{\\lambda}(L)$ , is thedimension of $\\ker(L-\\lambda I)$ , the eigenspace of $\\lambda$ .

单词	MultiplicityOfEigenvalue
释义	multiplicity of eigenvalue Suppose $V$ is a finite dimensional vector space over a field $\\mathbbmss{F}$ ,and suppose $L\\colon V\\to V$ is a linear map.Suppose also that $\\lambda\\in\\mathbbmss{F}$ is aneigenvalue of $L$ , that is, $\\operatorname{det}(L-\\lambda I)=0$ . The algebraic multiplicity,denoted by $A_{\\lambda}(L)$ , of $\\lambda$ is the multiplicity of the root $\\lambda$ to the polynomial $\\operatorname{det}(L-\\lambda I)=0$ .The geometric multiplicity of $\\lambda$ , denoted by $G_{\\lambda}(L)$ , is thedimension of $\\ker(L-\\lambda I)$ , the eigenspace of $\\lambda$ .
随便看	Multiplicity multiplicity MultiplicityOfEigenvalue multiplicity of eigenvalue MultiplyPerfectNumber multiply perfect number MultiplyPerfectNumbersPage Multiply Perfect Numbers Page MultiplyTransitive multiply transitive MultiresolutionAnalysis multiresolution analysis Multiset multiset Multisieve multisieve MultivaluedFunction multivalued function MultivariateDistributionFunction multivariate distribution function MultivariateGammaFunctioncomplexvalued multivariate gamma function (complex-valued) MultivariateGammaFunctionrealvalued multivariate gamma function (real-valued) MunnTree