@misc{10498/28708,
year = {2022},
url = {http://hdl.handle.net/10498/28708},
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.},
publisher = {AMER INST MATHEMATICAL SCIENCES-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 Lozano, Almudena del Pilar and García Pacheco, Francisco Javier and Mengibar-Rodríguez, Míriam and Sánchez Alzola, Alberto},
}