黑龙江大学自然科学学报
黑龍江大學自然科學學報
흑룡강대학자연과학학보
JOURNAL OF NATURAL SCIENCE OF HEILONGJIANG UNIVERSITY
2004年
4期
22-27
,共6页
Hadamard积%逆M-矩阵%三对角线矩阵%五对角线矩阵
Hadamard積%逆M-矩陣%三對角線矩陣%五對角線矩陣
Hadamard적%역M-구진%삼대각선구진%오대각선구진
Hadamard product%inverse M-matrix%tridiagonal%five-diagonal
令M-1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-矩阵的集合.首先证得:如果A,BM-1分别是上、下Hessenberg矩阵,则对任意H1,H2S2,AoB和(AoH1)o(BoH2)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满足对任意i-j3,aji=bij=0,则对任意H1,H2S3,AoB和(AoH1)o(BoH2)都是五对角线逆M-矩阵.
令M-1記所有n×n逆M-矩陣的集閤,Sk記所有實矩陣其每箇kk主子矩陣都是逆M-矩陣的集閤.首先證得:如果A,BM-1分彆是上、下Hessenberg矩陣,則對任意H1,H2S2,AoB和(AoH1)o(BoH2)都是三對角線矩陣(因而是完全非負矩陣);其次證得:如果A=(Aij),B=(bij)M-1滿足對任意i-j3,aji=bij=0,則對任意H1,H2S3,AoB和(AoH1)o(BoH2)都是五對角線逆M-矩陣.
령M-1기소유n×n역M-구진적집합,Sk기소유실구진기매개kk주자구진도시역M-구진적집합.수선증득:여과A,BM-1분별시상、하Hessenberg구진,칙대임의H1,H2S2,AoB화(AoH1)o(BoH2)도시삼대각선구진(인이시완전비부구진);기차증득:여과A=(Aij),B=(bij)M-1만족대임의i-j3,aji=bij=0,칙대임의H1,H2S3,AoB화(AoH1)o(BoH2)도시오대각선역M-구진.
Let M-1 be the set of all n × n inverse M-matrices; Sk be the set of all n × n real mattrices A such that each k × k principal submatrix of A is an inverse M-matrix. It is shown that:(i) if A, B ∈ M-1 are lower, upper Hessenberg matrices, respectively, then A o B and (A o H1) o (B o H2) are tridiagonal inverse M-matrices which are tot ally nonnegative for any H1,H2 ∈ S2; and (ii) if A = (aij),B = (bij) ∈ M-1 satisfy aji = bij = 0, for all i-j ≥ 3, then AoB and (A o H1) o (B o H2) are five-diagonal inverse M-mattrices for any H1, H2 ∈ S3.
