Interactions Between the Generalized Hadamard Product and the Eigenvalues of Symmetric Matrices

Details Interactions Between the Generalized Hadamard Product and the Eigenvalues of Symmetric Matrices Interactions Between the Generalized Hadamard Product and the Eigenvalues of Symmetric Matrices

2004-04-19

arxiv.org/abs/math/0404348v1

Mathematics

Optimization and Control

25 pages

Scientific paper

In [8] a notion of generalized Hadamard product was introduced. We show that when certain kinds of tensors interact with the eigenvalues of symmetric matrices the resulting formulae can be nicely expressed using the generalized Hadamard product and two simple linear operations on the tensors. The Calculus-type rules developed here will be used in [9] to routinize, to a large extend, the differentiation of spectral functions. We include all the necessary definitions and results from [8] on the generalized Hadamard product to make the reading self-contained.

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