A supporting vector of a matrix A for a certain norm \(\Vert \cdot \Vert \) on \(\mathbb {R}^n\) is a vector x such that \(\Vert x\Vert =1\) and \(\Vert Ax\Vert =\Vert A\Vert =\displaystyle \max _{\Vert y\Vert =1}\Vert Ay\Vert \). In this manuscript, we characterize the existence of supporting vectors in the infinite-dimensional case for both the \(\ell _1\)-norm and the \(\ell _{\infty }\)-norm. Besides this characterization, our theorems provide a description of the set of supporting vectors for operators on \(\ell _{\infty }\) and \(\ell _1\). As an application of our results in the finite-dimensional case for both the \(\ell _1\)-norm and the \(\ell _{\infty }\)-norm, we study meteorological data from stations located on the province of Cádiz (Spain). For it, we consider a matrix database with the highest temperature deviations of these stations.

一矩阵的支撑矢量甲一定范数\（\ Vert的\ CDOT \ Vert的\）上\（\ mathbb {R} ^ N \）是一个矢量X，使得\（\ Vert的X \韦尔= 1 \）和\（\ Vert Ax \ Vert = \ Vert A \ Vert = \ displaystyle \ max _ {\ Vert y \ Vert = 1} \ Vert Ay \ Vert \）。在此手稿中，我们描述了\（\ ell _1 \）-范数和\（\ ell _ {\ infty} \）-范数在无限维情况下支持向量的存在。除了这种表征之外，我们的定理还为\（\ ell _ {\ infty} \）和\（\ ell _1 \）上的运算符提供了一组支持向量的描述。。作为\（\ ell _1 \）-范数和\（\ ell _ {\ infty} \）-范数在有限维情况下的结果的应用，我们研究了来自省内各站点的气象数据加的斯（西班牙）的地图。为此，我们考虑具有这些站最高温度偏差的矩阵数据库。