CAJ | 학술논문

设K是一个体, K_(m×n)表示m×n上所有K矩阵的集合.对矩阵A∈K 若存在矩阵X∈K_(n×n)使AXA=A,XAX=X,AX=XA,则称X为A的群逆.研究分块矩阵广义逆的表达式是矩阵广义逆理论中研究的重要问题.分块矩阵的群逆表达式在奇异微分和差分方程、马尔可夫链、迭代方法和密码学等领域有广泛应用.这里给出了体上分块矩阵[ABB0](A,B∈K_(n×n),B~2=B,((I-B)A)~#存在)的群逆的存在性及表示形式.
설K시일개체, K_(m×n)표시m×n상소유K구진적집합.대구진A∈K 약존재구진X∈K_(n×n)사AXA=A,XAX=X,AX=XA,칙칭X위A적군역.연구분괴구진엄의역적표체식시구진엄의역이론중연구적중요문제.분괴구진적군역표체식재기이미분화차분방정、마이가부련、질대방법화밀마학등영역유엄범응용.저리급출료체상분괴구진[ABB0](A,B∈K_(n×n),B~2=B,((I-B)A)~#존재)적군역적존재성급표시형식.
Suppose K is a skew field and K~(n×n) is the set of all the n×n matrices over K. For A∈K~(n×n) if there exists a matrix X∈K~(n×n) satisfying the matrix equations AXA=A,XAX=X,AX=XA , then we call X the group inverse of A . Research on representations of the generalized inverses is an important problem in the theory of generalized inverses of matrices. The group inverse of block matrices has important applications in singular differential and difference equations, Markov chains, iterative methods, cryptography and so on. The existence and the representation of the block matrix [AB B0] (A,B∈K~(n×n),B~2=B,((I-B)A)~# wexists)are given in this paper.