@misc{10481/78227,
year = {2022},
month = {10},
url = {https://hdl.handle.net/10481/78227},
abstract = {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.},
organization = {Spanish Government	FEDER-UCA18-105867},
organization = {ERDF Operational Programme},
organization = {University of the Regional Government of Andalusia		
PGC-101514-B-I00},
publisher = {AIMS},
keywords = {Bounded linear operator},
keywords = {Hilbert space},
keywords = {Mean operator},
keywords = {Principal components},
keywords = {Supporting vector},
title = {Supporting vectors vs. principal components},
doi = {10.3934/math.2023100},
author = {Márquez, Almudena P. and Mengíbar Rodríguez, Míriam},
}