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Higher order derivatives and norms of certain matrix functions

Tese de doutoramento, Matemática (Álgebra Lógica e Fundamentos), Universidade de Lisboa, Faculdade de Ciências, 2014 ; In this thesis we obtain formulas for higher order directional derivatives for the immanant map, which is a generalization of the determinant and the permanent maps. We also obtain formulas for the k-th derivative of the m-th Х-symmetric tensor power of an operator or a matrix, where Х is an i...