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	Minkowski inequality MinkowskisConstant MinkowskiSpace Minkowski space MinkowskisTheorem MinkowskiSum Minkowski sum Minkowski’s constant Minkowski’s theorem MinorofAGraph minor (of a graph) MinorofAMatrix minor (of a matrix) MinusOneTimesAnElementIsTheAdditiveInverseInARing minus one times an element is the additive inverse in a ring MiquelPoint Miquel point MiracleOctadGenerator miracle octad generator MirrorImageOfAKnot mirror image of a knot MittagLefflerFunction Mittag-Leffler function MittagLefflersTheorem Mittag-Leffler’s theorem