【導讀】Volume73,Number246,Pages653{657. S0025-5718(03)01591-6. FORTHEINVERSE. i. jb. ii. j=. n. X. j=1. j6=i. jb. ij. j;i=1;:::;n;where0i. <1;i=1;:::;n;with=max. 1in. i. :Weshowthatno. 1. :More-. 1.Introduction. 2.Preliminaryfacts. LetA2M. n. ):The. Schurplement.grantOGP0008111.653. Lemma1.LetA2M. n. 1. :Letbea. subsetoff1;:::;ng:Theinequality. (1)jdetAjjdetA()jjdetA(0. )j. (2)jdetBjjdetB()jjdetB(0. )j. detB=. 1. detA. detB()=. detA(0. detA. detB(0. detA(). detA. :. inBandA(seeformula(33)in[2,Chapter1]).WesaythatB2M. n. short)if. (3)i. jb. ii. j=. n. X. j=1. j6=i. jb. ij. j;i=1;:::;n;where0i. <1;i=1;:::;n:Thequantity. (4)=max. 1in. i. 1. =A=(a. ij. ):Then,fori=1;:::;n;(5)jdetBj(1+i. )jb. ii. jjB. i. j;whereB. i. isthecofactorofb. ii. ,and. (6)ja. ji. jj. ja. ii. j;j6=i: