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.
References in periodicals archive ?
Using Kronecker coefficients we prove in [PP-u] the following extension of Sylvester's theorem.
Moreover, [p.sub.n](l, m, 0) = [p.sub.n](l, m) and therefore, for r = 0, Theorem 1.5 gives the unimodality of q-binomial coefficients, and hence a new (up to our knowledge) proof of Sylvester's theorem. Moreover, the other known algebraic proofs do not imply such results.
So, Sylvester's theorem can be applied to all of them.