Sylvester's Formula
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High Quality Content by WIKIPEDIA articles! ShorttitleIn matrix theory, Sylvester's formula or Sylvester's matrix theorem (named after J. J. Sylvester) expresses an analytic function f(A) of a matrix A in terms of the eigenvalues and eigenvectors of A. It states thatSylvester's formula applies for any diagonalizable matrix A with k distinct eigenvalues, 1, , k, and any function f defined on some subset of the complex numbers such that f(A) is well defined. The last condition means that every eigenvalue i is in the domain of f, and that every eigenvalue i with multiplicity mi 1 is in the…mehr

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High Quality Content by WIKIPEDIA articles! ShorttitleIn matrix theory, Sylvester's formula or Sylvester's matrix theorem (named after J. J. Sylvester) expresses an analytic function f(A) of a matrix A in terms of the eigenvalues and eigenvectors of A. It states thatSylvester's formula applies for any diagonalizable matrix A with k distinct eigenvalues, 1, , k, and any function f defined on some subset of the complex numbers such that f(A) is well defined. The last condition means that every eigenvalue i is in the domain of f, and that every eigenvalue i with multiplicity mi 1 is in the interior of the domain, with f being (mi 1) times differentiable at i.