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Let A → Ar be the map that takes a positive definite matrix to its rth power, and let DAr be the Fréchet derivative of this map. It is known that ∥DAr∥ = ∥rAr−1∥ if r ≤ 1 or if r ≥ 2, and also that ...

In this paper we derive two formulas for divided differences of a function of a function. Both formulas lead to other divided difference formulas, such as reciprocal and quotient rules. The two ...