@article{Márquez2023, 
author = {Almudena P. Márquez and Francisco Javier García-Pacheco and Míriam Mengibar-Rodríguez and Alberto Sánchez-Alzola},
title = {Supporting vectors vs. principal components},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {1937-1958},
keywords = {bounded linear operator, Hilbert space, mean operator, principal components, supporting vector},
url = {https://www.sciopen.com/article/10.3934/math.2023100},
doi = {10.3934/math.2023100},
abstract = {Let    T  :  X  →  Y be a bounded linear operator between Banach spaces    X  ,  Y. A vector        x    0    ∈                    S              X   in the unit sphere                      S              X   of    X is called a supporting vector of    T provided that    ‖  T  (      x    0    )  ‖  =  sup  {  ‖  T  (  x  )  ‖  :  ‖  x  ‖  =  1  }  =  ‖  T  ‖. 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.}
}