In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign...In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign pattern matrix (or sign pattern).For a re-al matrix B,by sgn (B) we mean the sign pattern matrix in which each positive (respec-tively,negative,zero) entry of B is replaced by+(respectively,-,0).If A is an展开更多
For a symmetric sign pattern S1 the inertia set of S is defined to be the set of all ordered triples si（S） = {i（A） ： A = A^T ∈ Q（S）} Consider the n × n sign pattern Sn, where Sn is the pattern with zero e...For a symmetric sign pattern S1 the inertia set of S is defined to be the set of all ordered triples si（S） = {i（A） ： A = A^T ∈ Q（S）} Consider the n × n sign pattern Sn, where Sn is the pattern with zero entry （i,j） for 1 ≤ i = j ≤ n or｜i -j｜=n- 1 and positive entry otherwise. In this paper, it is proved that si（Sn） = {（n1, n2, n - n1 - n2）｜n1≥ 1 and n2 ≥ 2} for n ≥ 4.展开更多
文摘In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign pattern matrix (or sign pattern).For a re-al matrix B,by sgn (B) we mean the sign pattern matrix in which each positive (respec-tively,negative,zero) entry of B is replaced by+(respectively,-,0).If A is an
基金The NSF(10871188)of Chinathe NSF(KB2007030)of Jiangsu Provincethe NSF(07KJD110702)of University In Jiangsu Province.
文摘For a symmetric sign pattern S1 the inertia set of S is defined to be the set of all ordered triples si（S） = {i（A） ： A = A^T ∈ Q（S）} Consider the n × n sign pattern Sn, where Sn is the pattern with zero entry （i,j） for 1 ≤ i = j ≤ n or｜i -j｜=n- 1 and positive entry otherwise. In this paper, it is proved that si（Sn） = {（n1, n2, n - n1 - n2）｜n1≥ 1 and n2 ≥ 2} for n ≥ 4.
