| 五对角线逆M-矩阵的Hadamard积 |
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| 引用本文： | 杨尚俊,吕敏.五对角线逆M-矩阵的Hadamard积[J].中国科学技术大学学报,2004,34(6):661-667. |
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| 作者姓名： | 杨尚俊 吕敏 |
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| 作者单位： | 1. 安徽大学数学系,安徽,合肥,230026
2. 中国科学技术大数学系,安徽,合肥,230026 |
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| 基金项目： | NationalNaturalScienceFoundationofChina(60375010). |
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| 摘 要： | 令M-1记所有n×n逆M矩阵的集合,Sk(k>1)记所有实矩阵其每个k×k主子矩阵都是逆M矩阵的集合.首先证得如果A,B∈M-1分别是上、下Hessenberg矩阵,则对任意H1,H2∈S2,AB和(AH1)(BH2)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-1满足aji=bij=0,i-j≥3,则对任意H1,H2∈S3,AB和(AH1)(BH2)都是五对角线逆M矩阵.
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| 关 键 词： | Hadmard积 逆M-矩阵 三对角线的 Hessenerg矩阵 五对角线的 |
Hadamard Product for Five-diagonal Inverse M-matrices |
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| Abstract.Hadamard Product for Five-diagonal Inverse M-matrices[J].Journal of University of Science and Technology of China,2004,34(6):661-667. |
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| Authors: | Abstract |
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| Abstract: | Let M-1 be the set of all n × n inverse M-matrices; Sk be the set of all n × n real matrices A such that each k × k principal submatrix of A is in M-1. Firstly we show that:if A,B ∈ M-1 are lower and upper Hessenberg matrices,respectively,then A . B and (A . H1 ) . (B . H2) are tridiagonal inverse M-matrices which are to tally nonnegative for any H1 ,H2 ∈ S2. Secondly we show that: if A = (aij) ,B=(bij) ∈ M-1 satisfy aji = bij = 0,(A)i-j≥3, thenA. Band(A. H1) . (B. H2) are five-diagonal inverse M-matrices forany H1, H2 ∈ S3. |
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| Keywords: | Hadamard product inverse M-matrix tridiagonal Hessenberg matrix five-diagonal |
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