On the nonsingularity of principal submatrices of a random orthogonal matrix (Q1066542)

Let S be a random \(p\times p\) non-negative definite matrix with a distribution which is absolutely continuous with respect to the Lebesgue measure and let G be an orthogonal matrix such that \(S=GDG'\) where D is the diagonal matrix with the eigenvalues of S along the diagonal in non- increasing order. In this paper it is proved that G has non-singular principal submatrices almost surely.