The vector of weights of an interpolatory quadrature rule with n preassigned nodes is shown to be the least-squares solution of an overdetermined linear system called the fundamental system of the rule. It is established the relation between and the minimax solution of the fundamental system and shown a certain invariance property for the norm of the residual vectors depending on the principal moment of the rule. In order to assess the main properties of a rule or to compare distinct rules, several parameters are defined such the angle of a rule  angle between  and  The referred parameters are tested on some Newton-Cotes, Fejér, Clenshaw-Curtis and Gauss-Legendre rules.

quadrature rule, least-squares solution, minimax solution, principal moment.