5 Jan
2007
5 Jan
'07
9:22 p.m.
On 1/6/07, N. J. A. Sloane <njas@research.att.com> wrote:
... This "robust" property is relevant when doing an LU decomposition of a matrix, so it may have a more official name (besides "all principal submatrices are nonsingular", I mean).
I'm struck by the fact that an analogous condition --- applied to the Cayley-Menger array of squared distances between pairs of vertices, bordered by an extra vertex (at infinity) whose distance from all the other points is constant --- is nec and suf for a simplex with n+1 vertices to be properly realisable in Euclidean n-dimensional space. Evidently this must be a significant property of a matrix, but I've not seen it christened before. WFL