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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.