Autor:	Pavlov, Dmitrii
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Computer Science - Symbolic Computation
Druh dokumentu:	Working Paper
Popis:	A positive definite matrix is called logarithmically sparse if its matrix logarithm has many zero entries. Such matrices play a significant role in high-dimensional statistics and semidefinite optimization. In this paper, logarithmically sparse matrices are studied from the point of view of computational algebraic geometry: we present a formula for the dimension of the Zariski closure of a set of matrices with a given logarithmic sparsity pattern, give a degree bound for this variety and develop implicitization algorithms that allow to find its defining equations. We illustrate our approach with numerous examples. Comment: 15 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.10042 Zobrazit plný text záznamu View this record from Arxiv