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
2011年
2期
196-199
,共4页
除环%指标%Drazin逆
除環%指標%Drazin逆
제배%지표%Drazin역
skew field%index%Drazin inverse
设K为除环,Kmxn是K上所有mxn矩阵的集合.设A∈Kmxn,满足rank(As+1)=rank(As)的最小非负整数s称为A的指标,记作Ind(A)=s.设A∈Kmxn,Ind(A)=s,如果X∈Knxn满足以下方程:(1)AXA=X(2)AX=XA(3)As+1X=As,则称为X为A的Drazin逆,记作X=AD.利用Fitting分解的方法,研究除环上分块矩阵(AO BC)的指标和Drazin逆的表示.
設K為除環,Kmxn是K上所有mxn矩陣的集閤.設A∈Kmxn,滿足rank(As+1)=rank(As)的最小非負整數s稱為A的指標,記作Ind(A)=s.設A∈Kmxn,Ind(A)=s,如果X∈Knxn滿足以下方程:(1)AXA=X(2)AX=XA(3)As+1X=As,則稱為X為A的Drazin逆,記作X=AD.利用Fitting分解的方法,研究除環上分塊矩陣(AO BC)的指標和Drazin逆的錶示.
설K위제배,Kmxn시K상소유mxn구진적집합.설A∈Kmxn,만족rank(As+1)=rank(As)적최소비부정수s칭위A적지표,기작Ind(A)=s.설A∈Kmxn,Ind(A)=s,여과X∈Knxn만족이하방정:(1)AXA=X(2)AX=XA(3)As+1X=As,칙칭위X위A적Drazin역,기작X=AD.이용Fitting분해적방법,연구제배상분괴구진(AO BC)적지표화Drazin역적표시.
Let Km×n be the set of all m×n matrices over a skew field K. The smallest nonnegative integer s satisfying rank (As+1) = rank (As) is called the index of the matrix A in Kmxn, and is denoted by Ind(A) =s.Let A∈Kn×n, if X∈Kn×n satisfies the equations: (1)XAX=X; (2)AX=XA; (3)As+1X = As, where Ind(A) = s, then X is called the Drazin inverse of A, and is denoted by X = AD.The index and the Drazin inverse of partitioned matrix (A B O C) over a skew field are researched by using the method of Fitting factorization.
