where x and y are vectors corresponding to x and y in the preceding equation for d(x,y). Often,it is necessary to compute a set of Euclidean distances between a vector y and each member of a vector population consisting of p,n dimensional vectors arranged as the row of a pXn matrix X for the dimentions to line up properly,y has to be of dimension 1Xn. Then the distance between y and each element of X is contained in the pX1 vector