Generalized Hadamard Product and the Derivatives of Spectral Functions
نویسندگان
چکیده
منابع مشابه
Generalized Hadamard Product and the Derivatives of Spectral Functions
In this work we propose a generalization of the Hadamard product between two matrices to a tensor-valued, multi-linear product between k matrices for any k ≥ 1. A multi-linear dual operator to the generalized Hadamard product is presented. It is a natural generalization of the Diag x operator, that maps a vector x ∈ R into the diagonal matrix with x on its main diagonal. Defining an action of t...
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A spectral function of a Hermitian matrix X is a function which depends only on the eigenvalues of X, 1 (X) 2 (X) : : : n (X), and hence may be written f(1 (X); 2 (X); : : :; n (X)) for some symmetric function f. Such functions appear in a wide variety of matrix optimization problems. We give a simple proof that this spectral function is diierentiable at X if and only if the function f is diier...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2006
ISSN: 0895-4798,1095-7162
DOI: 10.1137/050623206