纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2012年
6期
719-727
,共9页
矩阵方程%自反矩阵%广义奇异值分解%最小秩解%最佳逼近
矩陣方程%自反矩陣%廣義奇異值分解%最小秩解%最佳逼近
구진방정%자반구진%엄의기이치분해%최소질해%최가핍근
matrix equation%reflexive matrix%generalized singular value decomposition%minimal rank%optimal approximation
利用矩阵对的广义奇异值分解,得到了矩阵方程AX =B 有自反解的充分必要件,以及有解时,定秩解、最小秩解的一般表达式.另外,给出了自反最小秩解集合中与给定矩阵的最佳逼近解.
利用矩陣對的廣義奇異值分解,得到瞭矩陣方程AX =B 有自反解的充分必要件,以及有解時,定秩解、最小秩解的一般錶達式.另外,給齣瞭自反最小秩解集閤中與給定矩陣的最佳逼近解.
이용구진대적엄의기이치분해,득도료구진방정AX =B 유자반해적충분필요건,이급유해시,정질해、최소질해적일반표체식.령외,급출료자반최소질해집합중여급정구진적최가핍근해.
By applying the generalized singular value decomposition of matrix pairs, the necessary and su?cient conditions are obtained for the existence of the reflexive solutions of the matrix equation AX = B, and the expression of the fixed and minimal rank solutions is also shown. In addition, for the minimal rank solution set, the expression of the optimal approximation solution to a given matrix is derived.
