[math-fun] Q. about {0,1}-matrices.
Dear MathFun, SeqFans: Could anyone extend this sequence? %I A125587 %S A125587 1,4,68,5008 %N A125587 Call an n X n matrix robust if the top left i X i submatrix is invertible for all i = 1...n. Sequence gives number of n X n robust real {0,1}-matrices. %e A125587 a(2) = 4: %e A125587 10 10 11 11 %e A125587 01 11 01 10 %O A125587 1,2 %Y A125587 Cf. A125586. %K A125587 nonn,more %A A125587 njas and Vinay Vaishampayan (vinay(AT)research.att.com), Jan 05 2007 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). Neil
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
participants (2)
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Fred lunnon -
N. J. A. Sloane