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Generalized eigenvector

In linear algebra, a generalized eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria which are more relaxed than those for an (ordinary) eigenvector.

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Overview

Overview and definition

Examples

Canonical basis

  • Ranks Rank (linear algebra)

Computation of generalized eigenvectors

Jordan normal form

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Generalized eigenvector

Nodes55
Edges54
Triples17
Avg. degree1.96
Density0.036364
Components1

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Generalized eigenvector

Top relations

related to Generalized modal matrix · 4
Generalized eigenvector → All, All Jordan, Each, Let
related to Jordan chains · 4
Generalized eigenvector → Definition, Let, The, Thus
related to Canonical basis · 3
Generalized eigenvector → Definition, Jordan, Thus
related to Computation of generalized eigenvectors · 2
Generalized eigenvector → In, These
related to Example 5 · 2
Generalized eigenvector → In Example, Jordan
related to Examples · 2
Generalized eigenvector → Here, Some

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Important terminology

displaystyle matrix generalized lambda eigenvectors eigenvector basis mathbf eigenvalue form linearly independent jordan rank diagonal linear normal vector corresponding diagonalizable

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Generalized eigenvectorrelated to Canonical basisDefinition0.60section
Generalized eigenvectorrelated to Canonical basisJordan0.60section
Generalized eigenvectorrelated to Canonical basisThus0.60section
Generalized eigenvectorrelated to Computation of generalized eigenvectorsIn0.60section
Generalized eigenvectorrelated to Computation of generalized eigenvectorsThese0.60section
Generalized eigenvectorrelated to Example 5In Example0.60section
Generalized eigenvectorrelated to Example 5Jordan0.60section
Generalized eigenvectorrelated to ExamplesHere0.60section
Generalized eigenvectorrelated to ExamplesSome0.60section
Generalized eigenvectorrelated to Generalized modal matrixLet0.60section
Generalized eigenvectorrelated to Generalized modal matrixAll Jordan0.60section
Generalized eigenvectorrelated to Generalized modal matrixAll0.60section

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