数学季刊(英文版)
數學季刊(英文版)
수학계간(영문판)
CHINESE QUARTERLY JOURANL OF AMTHEMTICS
2002年
4期
62-68
,共7页
亚半正定%对称正定%广义奇异值分解
亞半正定%對稱正定%廣義奇異值分解
아반정정%대칭정정%엄의기이치분해
semipositive subdefinite%symmetric semipositie definite%generalized singualr value decomposition
本文给出了矩阵方程(Ⅰ)AXAT+BYBT=C,(Ⅱ)(ATXA,BTZB)=(C,D)有亚半正定解的充要条件.
本文給齣瞭矩陣方程(Ⅰ)AXAT+BYBT=C,(Ⅱ)(ATXA,BTZB)=(C,D)有亞半正定解的充要條件.
본문급출료구진방정(Ⅰ)AXAT+BYBT=C,(Ⅱ)(ATXA,BTZB)=(C,D)유아반정정해적충요조건.
Finding solutions of matrix equations in given set SRn×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively [2,3,4,5]. Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) [1,8]. In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in [2,3,4,5] in detail.
