Differentiability Properties of Isotropic Functions
نویسنده
چکیده
1. Introduction. Let Sym denote the linear space of all symmetric second-order tensors on an n-dimensional real vector space Vect with scalar product. (If Vect is identified with R n , then Sym may be identified with the set of all symmetric n-by-n matrices.) A function f : Sym → R is said to be isotropic if f (A) = f (QAQ T) for all A ∈ Sym and all Q proper orthogonals. An isotropic function has a representation f (A) = ˜ f (a), where˜f is a symmetric function on R n and a = (a 1 ,. .. , a n) are the
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