Calculation of the Weyr Characteristic from the Singular Graph of an M-matrix |
Contents
2 Standard Forms and the Singular Graph S | 4 |
3 Construction of an Sbasis for EA | 11 |
4 Relationship between wA and an Smatrix for A | 22 |
4 other sections not shown
Common terms and phrases
a-th column associated scalars B₁ B₂ block column ccrA combinatorially independent Corollary Daniel James Richman define Definition denote diagonal blocks DP+1 eigenspace E(A elementary divisor exist non-empty disjoint finite partially ordered following are equivalent full column rank Hence inductive assumption Jordan basis Ker AP Lemma Lemna Let vª level numbers linearly dependent linearly ordered M-matrix with singular Main Theorem non-empty disjoint subsets non-negative non-singular Observe p-th level partially ordered set permutation matrix Proof prove Q. E. D. Remark result follows Rothblum S-basis for E(A S-set satisfies condition 5.6ii Schneider 1956 semi-positive set with level singular graph singular matrix ß ɛ standard form suppose Theorem 4.7 thesis University of Wisconsin-Madison v₁ vectors w₁ Weyr characteristic αε αελ αεφ βα βε βελ γα λ₁ ΠΛ га