Supporting vectors vs. principal components

Autor:	Almudena P. Márquez, Francisco Javier García-Pacheco, Míriam Mengibar-Rodríguez, Alberto Sánchez-Alzola
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Principal components General Mathematics Supporting vector Hilbert space Mean operator Bounded linear operator
Popis:	Let T : X -> Y be a bounded linear operator between Banach spaces X, Y. A vector x(0) is an element of S-X in the unit sphere S-X of X is called a supporting vector of T provided that parallel to T(x(0))parallel to = sup{parallel to T(x)parallel to : parallel to x parallel to = 1} = parallel to T parallel to. Since matrices induce linear operators between finite-dimensional Hilbert spaces, we can consider their supporting vectors. In this manuscript, we unveil the relationship between the principal components of a matrix and its supporting vectors. Applications of our results to real-life problems are provided. Spanish Government FEDER-UCA18-105867 ERDF Operational Programme University of the Regional Government of Andalusia PGC-101514-B-I00
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b57818ec6b62a59c22011bc83c6adfb https://hdl.handle.net/10481/78227 Zobrazit plný text záznamu