Under any conditions, to change the inequality Sylvester into equation is the focus of the current study. This paper used thernλ matrix and its elementary transformation to correspond to the partitioned matrix diag{A+k1E, A+k2E, …, A+k1E) , so that when k1,k2,…,k1rnmeet certain conditions, there are t Σ t=1R(A+kiE)=tRΠ(A+kjE)+(t-l)n.%在何种条件下,Sylvester不等式化为等式是当前研究的重点.本文利用λ矩阵及其初等变换对应到分块矩阵diag{A+k1E,A+k2E,.,A+ktE}中,使得当k1,k2,…,k1在满足一定的条件时,有∑ti=1R(A+kiE)=R лti=1 (A+kiE)+(t-1)n.
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