About: Faddeev–LeVerrier algorithm

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In mathematics (linear algebra), the Faddeev–LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial of a square matrix, A, named after Dmitry Konstantinovich Faddeev and Urbain Le Verrier. Calculation of this polynomial yields the eigenvalues of A as its roots; as a matrix polynomial in the matrix A itself, it vanishes by the fundamental Cayley–Hamilton theorem. Computing determinant from the definition of characteristic polynomial, however, is computationally cumbersome,because is new symbolic quantity, whereas this algorithm works directly with coefficients of matrix .

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rdfs:label	Faddeev–LeVerrier algorithm (en)
rdfs:comment	In mathematics (linear algebra), the Faddeev–LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial of a square matrix, A, named after Dmitry Konstantinovich Faddeev and Urbain Le Verrier. Calculation of this polynomial yields the eigenvalues of A as its roots; as a matrix polynomial in the matrix A itself, it vanishes by the fundamental Cayley–Hamilton theorem. Computing determinant from the definition of characteristic polynomial, however, is computationally cumbersome,because is new symbolic quantity, whereas this algorithm works directly with coefficients of matrix . (en)
dbp:wikiPageUsesTemplate	dbt:= dbt:Math dbt:Mvar dbt:Reflist
Subject	Determinants Polynomials Homogeneous polynomials Linear algebra Mathematical physics Matrix theory
thumbnail	wiki-commons:Special:FilePath/Urbain_Le_Verrier.jpg?width=300
foaf:depiction
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Faddeev–LeVerrier_algorithm?oldid=1068150172&ns=0
Wikipage page ID	49598229 (xsd:integer)
page length (characters) of wiki page	12319 (xsd:nonNegativeInteger)
Wikipage revision ID	1068150172 (xsd:integer)
Link from a Wikipage to another Wikipage	Adjugate matrix Bell polynomials Urbain Le Verrier Determinants Polynomials Cayley–Hamilton theorem Fredholm determinant Jacobi's formula Homogeneous polynomials Linear algebra Mathematical physics Matrix theory Dmitry Faddeev Jean-Marie Souriau Characteristic polynomial Linear algebra Eigenvalues and eigenvectors Newton polynomial Exterior algebra Matrix (mathematics) Recurrence relation Resolvent formalism
has abstract	In mathematics (linear algebra), the Faddeev–LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial of a square matrix, A, named after Dmitry Konstantinovich Faddeev and Urbain Le Verrier. Calculation of this polynomial yields the eigenvalues of A as its roots; as a matrix polynomial in the matrix A itself, it vanishes by the fundamental Cayley–Hamilton theorem. Computing determinant from the definition of characteristic polynomial, however, is computationally cumbersome,because is new symbolic quantity, whereas this algorithm works directly with coefficients of matrix . The algorithm has been independently rediscovered several times, in some form or another. It was first published in 1840 by Urbain Le Verrier, subsequently redeveloped by P. Horst, Jean-Marie Souriau, in its present form here by Faddeev and Sominsky, and further by J. S. Frame, and others. (For historical points, see Householder. An elegant shortcut to the proof, bypassing Newton polynomials, was introduced by Hou. The bulk of the presentation here follows Gantmacher, p. 88.) (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Faddeev–LeVerrier_algorithm
is rdfs:seeAlso of	Cayley–Hamilton theorem Exterior algebra
is Wikipage redirect of	Faddeev-LeVerrier algorithm
is Link from a Wikipage to another Wikipage of	Adjugate matrix Cayley–Hamilton theorem Jacobi's formula Dmitry Faddeev Characteristic polynomial Newton's identities Faddeev-LeVerrier algorithm Determinant Invariants of tensors Massive gravity
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Faddeev–LeVerrier_algorithm

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