五对角线逆M-矩阵的Hadamard积(英文)

Hadamard product for inverse M-matrices of some special types

令M? 记所有n×n逆M-矩阵的集合,Sk记所有实矩阵其每个kk主子矩阵都是逆M-矩阵的 1集合. 首先证得: 如果A, BM? 分别是上、下Hessenberg矩阵, 则对任意H1, H2S2, A?B和(A?H1)?(B?H2) 1都是三对角线矩阵(因而是完全非负矩阵);其次证得: 如果A=(aij), B=(bij)M? 满足对任意i-j3, 1aji=bij=0, 则对任意H1, H2S3, A?B和(A?H1)?(B?H2) 都是五对角线逆M-矩阵.

Let M? be the set of all n × n inverse M-matrices; Sk be the set of all n × n real matrices A such that each 1 k × k principal submatrix of A is an inverse M-matrix. It is shown that:(i) if A,B ∈ M? are lower, upper Hessenberg 1 matrices, respectively, then A?B and (A?H1)?(B ?H2) are tridiagonal inverse M-matrices which are totally nonnegative for any H1,H2 ∈ S2; and (ii) if A = (aij),B = (bij) ∈ M? satisfy aji = bij = 0, for all i ? j ≥ 3, then A ? B and 1 (A ? H1) ? (B ? H2) are ?ve-diagonal inverse M-matrices for any H1,H2 ∈ S3.