Sabemos que un subespacio vectorial E ⊂ Rn x Rn puede ser expresado de dos formas distintas, como nUcleo y como imagen de transformaciones lineales, esto es E = {(x, x*) : Ax + Bx* = 0} y E = {(x, x*) : x = Pu, x* = Qu, u ϵ Rr} para algunas matrices A, B G Rpxn y P,Q G Rnxr. En este trabajo estudiaremos la relación entre ambas representaciones cuando el subespacio E es considerado monótono. Se establecerá esta relación por medio de las inercias de las matrices simétricas (ABt + BAt) y (PtQ + QtP).

The vehicle routing problem is one of the most studied problems in Operations Re-search. Different variants have been treated in the past 50 years and with technological advances, new challenges appear. In this thesis, we introduce a new variation of the VRP appearing in wireless networks. The new characteristic added to this well-know problem is the possibility of pick-up information via wireless transmissions. In the con-text considered here, a unique base station is connected with the outside and a vehicle is responsible for collecting information via wireless connection to the vehicle when it is located in another sufficiently close station. Simultaneous transmissions are permitted. Time of transmission depends on the distance between stations, the amount of infor-mation transmitted, and other physical factors (e.g obstacles along the way, installed equipment). Information to be sent...