2004/04/19 by Hristo S. Sendov, Sendov, Hristo S.
Computer Science · Mathematics · #15A69 #47A75 #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Spectral Theory (math.SP) #math.OC #math.SP #msc:15A18 #msc:15A69 #msc:47A75 #msc:49R50 #primary: 49R50 #secondary: 15A18
paper · pdf · doi:10.48550/arxiv.math/0404348
25 pages
arxiv created 2004/04/19 · openalex publication_date 2004/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.