  The supporting vectors of a matrix A are the solutions of max || x ||_2 =1
{||Ax||_2^2}. The generalized supporting vectors of matrices A_1 , . . . , A_k
are the solutions of max || x ||_2 =1 {||A_1x||_2^2 + ||A_2x||_2^2 + ... +
||A_kx||_2^2}. Notice that the previous optimization problem is also a boundary
element problem since the maximum is attained on the unit sphere. Many problems
in Physics, Statistics and Engineering can be modeled by using generalized
supporting vectors. In this manuscript we first raise the generalized
supporting vectors to the infinite dimensional case by solving the optimization
problem max || x || =1 sum_{i=1}^\infty ||T i (x )||^2 where (T i )_i is a
sequence ofbounded linear operators between Hilbert spaces H and K of any
dimension. Observe that the previous optimization problem generalizes the first
two. Then a unified MATLAB code is presented for computing generalized
supporting vectors of a finite number of matrices. Some particular cases are
considered and three novel examples are provided to which our technique
applies: optimized observable magnitudes by a pure state in a quantum
mechanical system, a TMS optimized coil and an optimal location problem using
statistics multivariate analysis. These three examples show the wide
applicability of our theoretical and computational model.
