Supporting vectors vs. principal components

<abstract><p>Let $ T:X\to Y be a bounded linear operator between Banach spaces X, $. A vector x_0\in {\mathsf{S}}_X in the unit sphere of X is called supporting T provided that \|T(x_0)\| = \sup\{\|T(x)\|:\|x\| 1\} \|T\| Since matrices induce operators finite-dimensional Hilbert spaces, we can consider their vectors. In this manuscript, unveil relationship principal components matrix and its Applications our results to real-life problems are provided.</p></abstract>