Browsing by Author "Freitas, Pedro J."
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- On derivatives and norms of generalized matrix functions and respective symmetric powersPublication . Carvalho, Sonia; Freitas, Pedro J.In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.
- The k-th derivatives of the immanent and the chisymmetric power of an operatorPublication . Carvalho, Sonia; Freitas, Pedro J.In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.
- The norm of the k-the derivative of the Chisymmetric power of an operatorPublication . Carvalho, Sonia; Freitas, Pedro J.In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained. This work is inspired in results by R. Bhatia, J. Dias da Silva, P. Grover, and T. Jain.