| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 1.01 MB | Adobe PDF |
Autores
Orientador(es)
Resumo(s)
As a generalization of the formulas proved by Bhatia, Grover and Jain (Derivatives of tensor powers and their norms. Electron J Linear Algebra. 2013;26:604-619), in recent papers (The kth derivative of the immannant and the chi-symmetric tensor power of an operator. Electron J Linear Algebra. 2014;27:Article 18, On derivatives and norms of generalized matrix functions and respective symmetric powers. Electron J Linear Algebra. 2015;30:Article 22) Carvalho and Freitas obtained formulas for directional derivatives, of all orders, for generalized matrix functions and for every symmetric tensor power associated with a character xi of a subgroup G of the symmetric group S-m. Throughout our work, we used some well-known formulas for the derivatives of all orders of a multilinear map, since the maps that we studied are all multilinear. In this paper, we intend to present an alternative proof of these formulas, using the multilinearity argument.
Descrição
Palavras-chave
Multilinear map Higher order derivatives Multilinearity argument
Contexto Educativo
Citação
CARVALHO, Sónia – An alternative proof on higher order derivatives of a multilinear map. Linear & Multilinear Algebra. ISSN 0308-1087. Vol. 68, N.º 7 (2020), pp. 1457-1464
Editora
Taylor & Francis