Sylvester's theorem

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Sylvester's theorem [sil′ves·tərz ‚thir·əm]

(mathematics)

IfAis a matrix with distinct eigenvalues λ₁,…,λ_n, then any analytic function ƒ(A) can be realized from the λ_i,ƒ(λ_i), and the matricesA- λ_iI, whereIis the identity matrix.

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