My web server - 3.3.4 THE SPECTRAL TEST 97 diagram makes this
3.3.4 THE SPECTRAL TEST 97 diagram makes this plain. (25) Turning to question (b), we want to choose the q2 so that U, +&+ qiiIJi has minimum length; geometrically, we want to start with Uj and add some vector in the (t -1)-dimensional hyperplane whose points are the sums of multiples of { Ui 1 i # j }. Again the best solution is to choose things so that Uj’ is perpendicular to the hyperplane, i.e., so that Uj . Uk = 0 for all k # j, i.e., U, . Uk + C qi(Ui ‘ uk) O? 1