Making matrices better: Geometry and topology of polar and singular value decomposition

Autor:	DeTurck, Dennis, Elsaify, Amora, Gluck, Herman, Grossmann, Benjamin, Hoisington, Joseph, Krishnan, Anusha M., Zhang, Jianru
Rok vydání:	2017
Předmět:	Mathematics - Rings and Algebras Mathematics - Numerical Analysis 15-02 15A18 15A23 15B10 (Primary) 53A07 55-02 57-02 57N12 91B24 91G30 92C55 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Our goal here is to see the space of matrices of a given size from a geometric and topological perspective, with emphasis on the families of various ranks and how they fit together. We pay special attention to the nearest orthogonal neighbor and nearest singular neighbor of a given matrix, both of which play central roles in matrix decompositions, and then against this visual backdrop examine the polar and singular value decompositions and some of their applications. Comment: 34 pages, 26 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1702.02131 Zobrazit plný text záznamu View this record from Arxiv