About: Sylvester's formula

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In matrix theory, Sylvester's formula or Sylvester's matrix theorem (named after J. J. Sylvester) or Lagrange−Sylvester interpolation expresses an analytic function f(A) of a matrix A as a polynomial in A, in terms of the eigenvalues and eigenvectors of A. It states that where the λi are the eigenvalues of A, and the matrices are the corresponding Frobenius covariants of A, which are (projection) matrix Lagrange polynomials of A.

Attributes	Values
rdfs:label	Fórmula de Sylvester (ca) Sylvester's formula (en) Формула Сильвестра (ru)
rdfs:comment	En teoria de matrius, la fórmula de Sylvester o teorema de matrius de Sylvester (en honor del matemàtic anglès J. J. Sylvester) o la interpolació de Lagrange−Sylvester expressa una analítica f(A) d'una matriu A com el polinomi en A, en termes dels valors propis i vectors propis de A. Diu el següent on les λi són els valors propis de A, i les matrius són els corresponents a A, que són la matriu (projecció) dels polinomis de Lagrange de A. (ca) In matrix theory, Sylvester's formula or Sylvester's matrix theorem (named after J. J. Sylvester) or Lagrange−Sylvester interpolation expresses an analytic function f(A) of a matrix A as a polynomial in A, in terms of the eigenvalues and eigenvectors of A. It states that where the λi are the eigenvalues of A, and the matrices are the corresponding Frobenius covariants of A, which are (projection) matrix Lagrange polynomials of A. (en) Формула Сильвестра, матричная теорема Сильвестера (названа именем Дж. Дж. Сильвестера) или интерполяция Лагранжа — Сильвестера выражает аналитическую функцию матрицы A как многочлен от A в терминах собственных значений и векторов матрицы A. Теорема гласит, что: где — собственные значения матрицы A, а матрицы являются соответствующими ковариантами Фробениуса матрицы A, которые являются матрицами (проекции) многочленов Лагранжа матрицы A. (ru)
dcterms:subject	Matrix theory
Wikipage page ID	8768758 (xsd:integer)
Wikipage revision ID	1082369042 (xsd:integer)
Link from a Wikipage to another Wikipage	Resolvent formalism Complex numbers Matrix (mathematics) Matrix function Frobenius covariant Matrix theory Adjugate matrix Felix Gantmacher Eigenvalue, eigenvector and eigenspace Hans Schwerdtfeger Hermite interpolation Hermitian matrix James Joseph Sylvester Holomorphic functional calculus Diagonalizable matrix Arthur Buchheim Unitary matrix Lagrange polynomials
sameAs	Sylvester's formula Sylvester's formula Sylvester's formula Sylvester's formula Sylvester's formula
dbp:wikiPageUsesTemplate	dbt:= dbt:Cite_book dbt:Cite_journal dbt:ISBN dbt:Math dbt:Mvar dbt:Reflist dbt:Rp
has abstract	En teoria de matrius, la fórmula de Sylvester o teorema de matrius de Sylvester (en honor del matemàtic anglès J. J. Sylvester) o la interpolació de Lagrange−Sylvester expressa una analítica f(A) d'una matriu A com el polinomi en A, en termes dels valors propis i vectors propis de A. Diu el següent on les λi són els valors propis de A, i les matrius són els corresponents a A, que són la matriu (projecció) dels polinomis de Lagrange de A. (ca) In matrix theory, Sylvester's formula or Sylvester's matrix theorem (named after J. J. Sylvester) or Lagrange−Sylvester interpolation expresses an analytic function f(A) of a matrix A as a polynomial in A, in terms of the eigenvalues and eigenvectors of A. It states that where the λi are the eigenvalues of A, and the matrices are the corresponding Frobenius covariants of A, which are (projection) matrix Lagrange polynomials of A. (en) Формула Сильвестра, матричная теорема Сильвестера (названа именем Дж. Дж. Сильвестера) или интерполяция Лагранжа — Сильвестера выражает аналитическую функцию матрицы A как многочлен от A в терминах собственных значений и векторов матрицы A. Теорема гласит, что: где — собственные значения матрицы A, а матрицы являются соответствующими ковариантами Фробениуса матрицы A, которые являются матрицами (проекции) многочленов Лагранжа матрицы A. (ru)
prov:wasDerivedFrom	wikipedia-en:Sylvester's_formula?oldid=1082369042&ns=0
page length (characters) of wiki page	6478 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Sylvester's_formula
is rdfs:seeAlso of	Analytic function of a matrix
is Link from a Wikipage to another Wikipage of	Quantum logic gate Pauli matrices List of scientific equations named after people Matrix exponential Eigendecomposition of a matrix Frobenius covariant Controlled NOT gate Lagrange polynomial Sylvester's theorem Cayley–Hamilton theorem Analytic function of a matrix James Joseph Sylvester Polynomial interpolation Square root of a matrix List of things named after James Joseph Sylvester Sylvester's matrix theorem Sylvester matrix theorem Lagrange-Sylvester interpolation Lagrange–Sylvester interpolation Lagrange−Sylvester interpolation
is Wikipage redirect of	Sylvester's matrix theorem Sylvester matrix theorem Lagrange-Sylvester interpolation Lagrange–Sylvester interpolation Lagrange−Sylvester interpolation
is known for of	James Joseph Sylvester
is foaf:primaryTopic of	wikipedia-en:Sylvester's_formula

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