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Frobenius normal form

In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained by conjugation by invertible matrices over F. The form reflects a minimal decomposition of the vector space into subspaces that are cyclic for A (i.e., spanned by some vector and its repeated…

Motivation, General case and theory & A rational normal form generalizing the Jordan normal form

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Motivation

Direct sumDiagonalizableEigenspacesEigenvaluesRoots
23 related topics

General case and theory

DegreeUnitsStructure theorem for finitely generated modules over a principal ideal domainQuotientIdeal
11 related topics

A rational normal form generalizing the Jordan normal form

Diagonal formLemme des noyauxFrCyclicBlock matrix
7 related topics

Overview

Linear algebraSquareMatrixFieldCanonical form
15 related topics

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General case and theory

A rational normal form generalizing the Jordan normal form

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Frobenius normal form

Nodes65
Edges64
Triples14
Avg. degree1.97
Density0.030769
Components1

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Frobenius normal form

Top relations

related to A rational normal form generalizing the Jordan normal form · 10
Frobenius normal form → For, Frobenius, It, Jordan, On, The, The Frobenius, There, These, This
related to Algorithms · 3
Frobenius normal form → Algorithm, An, Frobenius Normal FormAn Algorithm
is a · 1
Frobenius normal form → companion matrix of the characteristic polynomial

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Important terminology

form cyclic matrix polynomial rational minimal canonical normal subspaces one field characteristic decomposition vector matrices space frobenius polynomials jordan similar

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SubjectPredicateObjectConfidenceSrc
Frobenius normal formis acompanion matrix of the characteristic polynomial0.90text
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formThe Frobenius0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formThis0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formOn0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formFrobenius0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formJordan0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formFor0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formThere0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formIt0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formThese0.60section
Frobenius normal formrelated to A rational normal form generalizing the Jordan normal formThe0.60section
Frobenius normal formrelated to AlgorithmsAn0.60section

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