Supporting vectors vs. principal components Márquez, Almudena P. Mengíbar Rodríguez, Míriam Bounded linear operator Hilbert space Mean operator Principal components Supporting vector 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. 2022-12-01T12:08:05Z 2022-12-01T12:08:05Z 2022-10-26 info:eu-repo/semantics/article Almudena P. Márquez... [et al.]. Supporting vectors vs. principal components[J]. AIMS Mathematics, 2023, 8(1): 1937-1958. doi: [10.3934/math.2023100] https://hdl.handle.net/10481/78227 10.3934/math.2023100 eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional AIMS