RT journal article
T1 Supporting vectors vs. principal components
A1 Márquez Lozano, Almudena del Pilar
A1 García Pacheco, Francisco Javier
A1 Mengibar-Rodríguez, Míriam
A1 Sánchez Alzola, Alberto
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 bounded linear operator
K1 Hilbert space
K1 mean operator
K1 principal components
K1 supporting vector
AB 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.
PB AMER INST MATHEMATICAL SCIENCES-AIMS
SN 2473-6988
YR 2022
FD 2022
LK http://hdl.handle.net/10498/28708
UL http://hdl.handle.net/10498/28708
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 08-nov-2026