Sylvester's theorem

Sylvester's theorem

[sil′ves·tərz ‚thir·əm] (mathematics) If A is a matrix with distinct eigenvalues λ1,…,λn , then any analytic function ƒ(A) can be realized from the λi ,ƒ(λi ), and the matrices A- λi I, where I is the identity matrix.