tend to agree more than in the sample as a whole, the quantity S of Equation 4 will tend to be large. This is exactly what we maximize as a function of the vector e. More generally, if we have K distinct populations, there are K − 1 vectors constant on each population, summing to zero and linearly independent. This implies that, if the number of markers is sufficiently large, there will be K − 1 eigenvalues and K − 1 corresponding eigenvectors of our matrix that are significant and meaningful. Vectors orthogonal to these K − 1 vectors are showing within-population variance, and if each population is homogeneous, this is just reflecting sampling noise.
